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The optimal time to trade the forex foreign exchange market is when it's at its most active levels. That's when trading spreads the differences between bid prices and ask prices tend to narrow. In those situations, less money goes to the market makers facilitating currency trades, which leaves more money for the traders to pocket personally. Forex traders need to commit their hours to memory, with particular attention paid to the hours when two exchanges overlap. When more than one exchange is open at the same time, this increases trading volume and adds volatility—the extent and rate at which forex market schedule or currency prices change. The volatility can benefit forex traders. This may seem paradoxical.

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Log in with Facebook Log in with Google. Remember me on this computer. Enter the email address you signed up with and we'll email you a reset link. Need an account? Click here to sign up. Download Free PDF. Free PDF. PDF Pack. People also downloaded these PDFs. People also downloaded these free PDFs. Review: current international research into cellulose nanofibres and nanocomposites by Tue Simonsen.

Project Finance in Developing countries by Naimeh Masoumi. Jashim Ali Chowdhury, LL. De Roux A. The global history of liability regime is not static; rather, it is evolving. Liability regime is such a field where new development has been happening from time to time. China in this regards is not an exception. The largest environmental case ever prosecuted in Spain, brought thousands of plaintiffs who were claiming for different kind of damages and prejudices.

More than 2. As countries, it included Spain and France. The Prestige oil spill created a huge fuss in the international maritime society and of course, in the Spanish population and consequently in Europe. Pursuant to the largest disaster ever in Europe, laws were enacted and reviewed regarding oil spills.

As a product of those conventions, Maritime Labor Convention MLC provides detailed rights and protections to seafarers. However, China has not ratified MCL for certain reasons. Nevertheless, seafarers' protection has an emerging position in the pyramid Chinese legal systems. Besides, some sources of law for seafarers' protection in China are substantively identical to MCL On domestic seafarers' protection, legislatures, governmental authorities and NGO are making different efforts on narrowing the gap between standards in MLC and ones in China.

They, however, received significant attention from both Congress and the Supreme Court that helped ensure that the general aspiration of limited government is respected. In contrast, the ordinance-making power of the President of Bangladesh is an express and well-conditioned constitutional grant. This, unfortunately, is not matched by a comparable parliamentary and judicial engagement.

The paper, therefore, relies on a functional perspective of constitutionalism to argue that a constitution that reads well has important lessons to learn from a constitution that works well. Supreme Court upheld the year-old Basic v. It will conclude with recommendations for Uganda to adopt voluntary conservation easements as has been carried out in the U.

S to reduce our increasing vulnerability to landslides. After the recent discovery of offshore oil and gas in the Mediterranean Sea, this paper attempts to address whether Lebanon sustainably develop its oil and gas resources, and be spared the curse of plenty.

This includes an analysis of the allocation of liability in these cases, and how the partition of responsibility between civilians and organizations occurs. Being a multibillion-dollar activity,9 project finance is used repeatedly as a financing technique for construction of new energy infrastructure,10 particularly in construction of hydroelectric dams.

Gelder et al. See also supra note 3. Multilateral development banks still play an important role in funding large dams, but increasingly less in terms of their direct financial commitment. In the very outset, it was designed to be in the priority among other energy-projects, and always enjoyed increased attention from the Soviet Union USSR administration. For independent Tajikistan, the inherited construction of the Rogun hydroelectric plant is the light at the end of tunnel.

Tajikistan suffers from a critical need for winter electricity, with demand exceeding supply by up to 25 percent at present. Techno-economic assessments studies TEAS14 of the project that were conducted in cooperation and with financial support of the World Bank,15 examined four homogeneous financial models involving such fund sources as full government self-financing with equity, preferential loan from a foreign government, multilateral and commercial loans, and foreign bond issuance.

In its final report Key Issues for Consideration on the Proposed Rogun Hydropower Project, the World Bank recommended Tajikistan consider a hybrid alternative for the project financing purposes by combining four proposed elements in one structure. In our opinion, a properly chosen capital model of Rogun HEP is a key element that will be able not only to the financing question, but also to mitigate increasing political tensions between the host- project Tajikistan and the project-affected Uzbekistan.

Rogun Project Background Central Asia16 CA is a region where energy resources are distributed with high unequally17 Tajikistan and Kyrgyzstan are two countries in the upstream that lack both of oil and gas. Meanwhile their downstream neighbors, Turkmenistan, Kazakhstan, and Uzbekistan, possess a comparatively significant level of fuel reserves.

Nonetheless, Tajikistan and Kyrgyzstan are geographically blessed with enormous hydropower potential. In the past, these five countries were able to keep balancing their interests in energy and natural resources as long as they were bound together by mutual compensating obligations. The megawatt Rogun hydroelectric plant project in Tajikistan has a four-decade history of formation. According to Schmidt at al. Schmidt et al. The Vakhsh river basin, with a total drainage area of about 39, km2, is located in the highest part of Middle Asia within the Pamir-Altai Mountains.

Downstream the confluence of the Vakhsh and the Pyanj, the river is called Amu- Darya. See supra note During , first a feasibility study and then the design for construction of Rogun HEP project were developed. Preparatory construction works commenced in , and the main construction activities started during In , construction works were suspended because of the USSR collapse. See supra note 20, at pp. Contrary to the original purpose of the project, the present plan calls for Rogun to serve as a multi-purpose project providing power, flow regulation, flood control, and sediment retention.

Consultants in their assessment studies28 expand the favorable nature of the project with the following benefits: i downstream flow regulation potential; ii electricity production for export; iii flood routing; and iv retention of sediments. Project-Related Dispute between Riparians Construction of Rogun HEP began in and was then interrupted by political changes resulting from the independence of Tajikistan and the other CA countries.

Construction began again in , but since only care and maintenance activities have been carried out pending finalization of assessment studies mentioned above. Specifically, downstream Uzbekistan vehemently opposes the project, characterizing it as unsafe and arguing that it will provide Tajikistan with unfair control over water resources in the region. The project was suspended primarily because downstream Uzbekistan insisted on conducting an independent impact assessment of the project on downstream countries that would comprise all aspects of the project in the region, including social, environmental, technical, and economic impacts.

Subsequently, Tajikistan turned to the World Bank for financing such assessments on credit. Techno-Economic Assessment Study In response to a request by the government of Tajikistan, in the World Bank supported assessment studies29 to evaluate the viability of the proposed Rogun dam project. These studies are designed to examine the potential benefits and risks of the proposed HEP and comprehensively evaluate its technical, economic, social, and environmental viability, based on international standards and practices and in accordance with World Bank policies and procedures.

The TEAS summarizes the assumptions, approach, and results of financial analysis under the hypothetical case during forecast horizon from to This case adopts many of the planning assumptions used for the central case of the economic analysis.

They also consider a sensitivity in which construction cost overruns increase the capital expenditure 27 Supra note This analysis aims to identify a high-level range of funding possibilities for the project, subject to assumed costs for various potential sources. Generally, the term project financing is used to refer to a nonrecourse or limited recourse financing structure.

In developing countries, projects were financed by the government borrowing from the international banking market, development-finance institutions such as the World Bank, or through export credits. Basic Components Special Project Vehicle For the purposes of project financing, it is a general practice when a new entity is created and controlled by the sponsor s of a project.

It also is generally used for entering into all project-related contracts where it is indicated as a borrower of the debt funds raised for the project. Usually such entities are registered formed in the jurisdiction where the project is hosted, in accordance with the local laws and regulations. See also supra note 2. See also supra note With stress on international project financing, this paper singles out the following of them — the host government, the sponsors and the lenders — that are the main decision makers and whose decisions determine the overall structure and course of project development.

Hoffman defines the host government as the government of the country where a project is located,51 and often it is a key participant in various international project finance transactions,52 and whose decisions or lack of them significantly define the ultimate success of a project. Overall investment climate, regulatory regime, and political stability in the country, continuing support and level of cooperation in general are few in a long list of what the host government may impact.

I was wondering if you might be able to help me. I am trying to find a German polymath who might be happy to be interviewed on the below programme about Goethe and other notable German polymaths of the past. Primary focus will be on 18th and 19th century arts and culture ranging from Bach to Bauhaus, Beethoven to the Brandenburg Gate, Wagner to Weimar Classicism.

Hope we could stay in touch and exchange information eventually. Thanks for the blog and posts. That can be drawn by hand!?! Looks like I should make my mathematics study rapid so that I can also draw such amazing 8-D figures. Dear Sir! First time I read or heard or learnt about the word combinatorics at your site today.

It is almost a strange topic for me. But as I usually do, I planned to read about you and then to wander across posts of your site. Seems an ocean of knowledge. Let see how much knowledge I can carry…? Something unrelated to any specific post. It is Tanya instead of Tamya.

I am currently running a crowd funding campaign for my upcoming educational game Sweet Math. I was wondering what is the process to get a story out on your blog. Who is the guy sitting beside you in the picture above your blog?

He seems to be a mathematician. Sorry for my ignorance if he is a well-known person and my question is off-topic. My condolence. Matousek is dead. It is always hard to lose a thinking brain, particularly when it happens too soon.

I really admire your commemoration of the dead colleagues and acquaintances on your blog. We are currently running a campaign for one of the top online stationery brands that you and your readers might find very interesting. Please kindly write to me at helen anagraminteractive. I just recently stumbled on the Scott Aaronson Comment topic, and am reading through it. And, of course, like in our case here, suffering and great frustration from academic performance is not limited to those who are very disable but also to those who are able and are obsessed with wanting to achieve more.

I eventually got over this and had no problem flirting and etcetera as a something adult, and getting married at When it came to academics though, I internalized everything society was saying about school, studying, etc…. Without them you will never have opportunities to learn more. Plus grades are an actual indication of how much you have learned and retained.

No, those who invent and research in their teens are typically the children of working scientists or professionals who are being mentored by their parents or some family connection, or are in a special program only accessible by those living in big cities.

The prestigious universities have places for kids without these benefits. Said depression exacerbating the bad study habits and leading to dropping out of school entirely. It took 17 years and 5 institutions for me to finish a B. So thank you very much for not forgetting about people like me, and of course those with lesser intellectual gifts who have it even harder. You are commenting using your WordPress.

You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. Combinatorics and more. Skip to content. My homepage contains more information about my research, teaching, former students and collaborators, and some pictures, none of which is as symmetric as this one: Gosset polytope — a hand drawing by Peter McMullen of the plane projection of the 8-dimensional 4-simplicial 4-simple Gosset polytope.

Share this: Facebook Reddit Twitter. Like this: Like Loading March 22, at am. Gill, what do you use to generate the latex for your posts? April 16, at am. Gil Kalai says:. JCummings says:. October 14, at am. Gil, What do you use to generate your graphs? Thanks for your help and for this blog!

William Lee says:.

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To illustrate the difficulty, let me begin with two quotes which contradict each other in the most illuminating way. The subject of combinatorics is so vast that the author of a textbook faces a difficult decision as to what topics to include. There is no more-or-less canonical corpus as in such other subjects as number theory and complex variable theory.

Combinatorics is a very broad subject, so the difficulty in writing about the subject is not what to include, but rather what to exclude. Which hundred problems should we choose? Now that this is all clear, you can probably insert your own joke about importance of teaching inclusion-exclusion. But I think the issue is a bit deeper than that. You can see a complete divergence of points of view on how to answer this question.

Some make the definition or description to be very broad sometimes even ridiculously broad , some relatively narrow, some are overly positive, while others are revoltingly negative. This may seem puzzling, but if you concentrate on the narrow definitions and ignore the rest, a picture emerges. Clearly, these people are not talking about the same area. They are talking about sub-areas of Combinatorics that they know well, that they happen to learn or work on, and that they happen to like or dislike.

Somebody made a choice what part of Combinatorics to teach them. They made a choice what further parts of Combinatorics to learn. And they project their views of these parts of Combinatorics on the whole field. Combinatorics is just too broad of a category to describe. How should one resolve the issue raised above? I think the answer is simple.

Stop claiming that Combinatorics , or worse, Discrete Mathematics , is one subject. Combinatorics is comprised of many sub-areas, see the Wikipedia article I discussed here long ago. Just accept it. Especially to graduate students, but to undergraduates as well.

Whether introductory or advanced versions of these courses, there is plenty of material for each such course. In fact, this is a disservice to both the students and the area. Different students want to know about different aspects of Combinatorics. Thus, if you are teaching the same numbered undergraduate course every semester you can just split it into two or three, and fix different syllabi in advance.

The students will sort themselves out and chose courses they are most interested in. They are broader, in fact, than the titles suggest — see Math and Math here. The former turned out to be quite a bit more popular among many applied math and non-math majors, especially those interested in CS, engineering, data science, etc. Math majors tend to know a lot of this material and flock to the latter course.

I am not saying you should do the same — this is just an example of what can be done. We now use both at UCLA. There are also many good Graph Theory course textbooks of all levels, of course. Similarly, for graduate courses, make sure you make the subject relatively narrow and clearly defined.

Like a topics class, except accessible to beginning graduate students. Low entry barrier is an advantage Combinatorics has over other areas, so use it. To give examples from my own teaching, see unedited notes from my graduate courses:. Combinatorics of posets Fall Combinatorics and Probability on groups Spring Algebraic Combinatorics Winter Discrete and Polyhedral Geometry Fall This is based on my book. See also videos of selected topics in Russian. Combinatorics of Integer Sequences Fall Combinatorics of Words Fall Tilings Winter , lecture-by-lecture refs only.

In my experience, the more specific you make the combinatorics course the more interesting it is to the students. You create a good course and the students will quickly figure it out. They do have their own FB and other chat groups, and spread the news much faster than you could imagine…. Unfortunately, there is often no good textbook to cover what you want.

So you might have to work a little harder harder to scout the material from papers, monographs, etc. In the internet era this is easier than ever. In fact, many extensive lecture notes are already available on the web. Eventually, all the appropriate textbooks will be written. As I mentioned before , this is one of the very few silver linings of the pandemic…. Having said that, these voluminous textbooks can be incredibly valuable to both the students and the instructor as a source of interesting supplementary material.

The enormity of the university administration can instill fear. How can you possibly fight such a machine? Even if an injustice happened to you, you are just one person with no power, right? Well, I think you can. Whether you succeed in your fight is another matter.

But at least you can try… In this post I will try to give you some advise on how to do this. Wait for future blog posts otherwise…. Warning : Much of what I say is relevant to big state universities in the US. Who am I to write about this? It is reasonable to ask if any of this is based on my personal experience of fighting university bureaucracies. The answer is yes, but I am not willing to make any public disclosures to protect privacy of all parties involved.

Let me just say that over the past 20 years I had several relatively quiet and fairly minor fights with university bureaucracies some of which I won rather quickly by being right. Once, I bullied my way into victory despite being in the wrong as I later learned , and once I won over a difficult non-personal political issue by being cunning and playing a really long game that took almost 3 years. By contrast, when I tried to fight the federal government a couple of times on academic matters , I lost quickly and decisively.

They are just too powerful…. Should you fight? But probably not. Say, you complained to the administration about what you perceive to be an injustice to you or to someone else. Your complaint was denied. This is when you need to decide if you want to start a fight.

If you do, you will spend a lot of effort and on average probably lose. The administrations are powerful and know what they are doing. Can you fight? Yes, you can. You can win by being right and convince bureaucrats to see it this way. You can win by being persistent when others give up. You can also win by being smart. Big systems have weaknesses you can exploit, see below.

Use them. Is there a downside to winning a fight? In the process you might lose some friends, raise some suspicions from colleagues, and invite retribution. On a positive side, big systems have very little institutional memory — your win and the resulting embarrassment to administration will be forgotten soon enough.

Is there an upside to losing a fight? Actually, yes. You might gain resect of some colleagues as someone willing to fight. And if your cause is righteous, this might help your reputation in and beyond the department. Why did I fight? The injustice, as I perceived it, was eating me alive and I had a hunch there is a nonzero chance I would win.

There were cases when the issue was much too minor to waste my energy. Is there a cost of not fighting? Yes, and it goes beyond the obvious. First , fighting bureaucracy is a skill, and every skill takes practice. I remember when tried to rent an apartment in Cambridge, MA — some real estate agents would immediately ask if I go to Harvard Law School. Most of these lawsuits would quickly fail, but the legal proceeding were costly to the owners. Second , there is a society cost.

If you feel confident that your case is strong, you winning might set a precedent which could benefit many others. Know your adversary. Remember — you are not fighting a mafia, a corrupt regime or the whole society. Your adversary is a group of good people who are doing their jobs as well as they can. They are not infallible, but probably pretty smart and very capable when it comes to bureaucracy, so from game theory point of view you may as well assume they are perfect.

Know your rights. This might seem obvious, but you would be surprised to know how many academics are not aware they have rights in a university system. For example, Wikipedia is a large project which survived for 20 years, so unsurprisingly it has a large set of policies enforced by an army of admins. The same is probably true about your university and your department. Search on the web for the faculty handbook, university and department bylaws, etc.

Go through the motions. Say, you think you were slighted. Whatever it is, you are upset, I get it. Your first step is not to complain but go through the motions, and email inquiries. Email the head of the department, chair of the executive committee, your faculty dean, etc. Calmly ask to explain this decision. You win, case closed. Also, sometimes you either get a convincing explanation with which you might agree — say, the university is on salary freeze so nobody got a salary increase, see some link.

Again, case closed. These are the cases that you need to know how to handle and all such cases are a little different. I will try to cover as much territory as possible, but surely will miss some cases. Ask for advice. This is especially important if you are a junior mathematician and feel a little overwhelmed. Find a former department chair, perhaps professor emeritus, and have an quiet chat.

They might also suggest who else you should talk to that would be knowledgeable and help dealing with an issue. With friends like these, you are in a good shape. Come by for a chat. This is a standard move by a capable bureaucrat. You lost. There is only one way to counter this move. Agree to a meeting — play nice and you might learn something. This defeats the purpose of the meeting moving you back to square one. At the meeting do not agree with anything, never say yes or no to anything.

Do not sign anything. If offered a document to sign, take it with you. Get it all in writing. Within a few hours after the meeting, email to the bureaucrat an email with your notes. I am writing this to ensure there is no misunderstanding on my part. A capable bureaucrat will recognize the move and will never go on record with anything unbecoming. They will accept the out you offered and claim that you indeed misunderstood.

In lieu of the misunderstanding they will need to give a real answer to your grievance otherwise what was the point of the meeting? Sometimes a bureaucrat will still resort to platitudes, but now that they are in writing, that trick is harder to pull off, and it leads us to a completely different scenario see below.

Accept the win. If not, follow up about details. Accept the defeat. Remain calm. Power of CC. If you receive a non-answer full of platitudes or no email reply at all give it exactly one week , then follow up. I would really appreciate your response to [all issues I raised]. Most likely you will get a reply within hours.

This is extremely atypical and related to [your unusual circumstances]. While this is normally not appropriate, we are happy to make an exception in your case and [compensate you]. Now, there is only one way to counter this, as far as I know. The only way out is to pretend to be just as illogical as the bureaucrat pretends to be.

I gratefully accept your sincere apology and your assurances this will not happen again to me nor anyone else at the department. A capable bureaucrat will recognize they are fighting fire with fire. Now that seem overly defensive. And they would have to reply to the whole CC list again, which is not what they want. They are aware that everyone else knows they screwed up, so reminding everyone with a new email is not in their interest.

And there is a decent chance you might reply to the whole CC list again with all that sugarcoated unpleasantness. Shifting blame or responsibility. This is great news for you — a tacit validation of your cause and an example of a bureaucrat putting their own well-being ahead of the institution. Remember, your fight is not with X, but with the administration. Like with musical chairs, you might have to repeat the procedure a few times, but chances are someone will eventually accept responsibility just to stop this embarrassment from going circles.

By then, there will be so many people on the CC chain, your issue will be addressed appropriately. Help them help you. Sometimes a complaint puts the bureaucrat into a stalemate. They want to admit that injustice happened to you, but numerous university rules forbid them from acting to redress the situation. In order to violate these rules, they would have to take the case upstairs, which brings its own complications to everyone involved. Essentially you need to throw them a lifeline by suggesting some creative solution to the problem.

While the bureaucrat may not agree with your proposed solution, your willingness to deal without an apology will earn you some points and perhaps lead to a resolution favorable to all parties. It is a common misconception that university administrations are very slow and rigid. In reality, when they want to, such large systems can turn on a dime by quickly utilizing its numerous resources human, financial, legal, etc.

Making it public. Just about every time you make grievances public you lose some social points with people who will hold it against you, claim you brought it on yourself, etc. In the world of social media your voice will be drowned and your case will be either ignored or take life of its own, with facts distorted to fit a particular narrative. The administration will close ranks and refuse to comment. You might be worse off than when you started.

The only example I can give is my own combative blog post which remains by far my most widely read post. Everyone just loves watching a train wreck… Many people asked why I wrote it, since it made me a persona non grata in the whole area of mathematics. There is really nothing I can do and they know it. But you can very indirectly threaten to make it public. Low level university bureaucrats are not really afraid for their jobs. For example, head of the department might not even want to occupy the position, and is fully protected by tenure anyway.

But deans, provosts, etc. In this case I recommend you find an email of some student editor of a local university newspaper. I am confident there will be people on all sides who disagree collectively with just about every sentence I wrote. Remember — this blog post is a not a recommendation to do anything. Good luck everyone! Hope you will never have to deal with any of that!

In our math research we make countless choices. We chose a problem to work on, decide whether its claim is true or false, what tools to use, what earlier papers to study which might prove useful, who to collaborate with, which computer experiments might be helpful, etc. Choices, choices, choices… Most our choices are private.

Others are public. This blog is about wrong public choices that I made misjudging some conjectures by being overly pessimistic. As I have written before , conjectures are crucial to the developments of mathematics and to my own work in particular. The concept itself is difficult, however. To understand this, note the stark contrast with experimental physics, as many mathematical conjectures are not particularly testable yet remain quite interesting.

For example, if someone conjectures there are infinitely many Fermat primes , the only way to dissuade such person is to actually disprove the claim. There is also an important social aspect of conjecture making. For a person who poses a conjecture, there is a certain clairvoyance respected by other people in the area.

Predictions are never easy , especially of a precise technical nature, so some bravery or self-assuredness is required. Note that social capital is spent every time a conjecture is posed. Now, for the person working on a conjecture, there is also a betting aspect one cannot ignore.

As in, are you sure you are working in the right direction? The success in solving a well known conjecture is often regarded much higher than a comparable result nobody asked about. This may seem unfair, and there is a bit of celebrity culture here. Thinks about it this way — two lead actors can have similar acting skills, but the one who is a star will usually attract a much larger audience…. Not unlike what happens to papers and mathematical results , conjectures also have stories worth telling, even if these stories are rarely discussed at length.

Let me list a few scenarios, from the least to the most mathematically helpful:. Say, you are working on a major open problem. You realize that a famous conjecture A follows from a combination of three conjectures B , C and D whose sole motivation is their applications to A. Some of these smaller conjectures are beyond the existing technology in the area and cannot be checked computationally beyond a few special cases. Somebody points out that D is trivially false.

Everyone else shrugs and moves on. You are working in a major field of study aiming to prove a famous open problem A. Over the years you proved a number of special cases of A and became one the leaders of the area. You are very optimistic about A discussing it in numerous talks and papers. Suddenly A is disproved in some esoteric situations, undermining the motivation of much of your older and ongoing work. In your ongoing work you stumble at a coincidence. You are clueless why would that be true, since being nice belongs to another area X.

Being nice is also too abstract to be checked easily on a computer. So you mention it in the Final Remarks section of your latest paper in vain hope somebody reads it. You are doing computer experiments related to your work. Suddenly certain numbers appear to have an unexpectedly nice formula or a generating function. You check with OEIS and the sequence is there indeed, but not with the meaning you wanted. You think deeply about famous conjecture A.

Not only your realize that there is no way one can approach A in full generality, but also that it contradicts some intuition you have about the area. However, A was stated by a very influential person N and many people believe in A proving it in a number of small special cases. You want to state a non-A conjecture, but realize the inevitable PR disaster of people directly comparing you to N. You think deeply about the area and realize that there is a fundamental principle underlying certain structures in your work.

Formalizing this principle requires a great deal of effort and results in a conjecture A. Obviously, there are many other possible stories, while some stories are are a mixture of several of these. Turns out, over the years I made a lot of those. Even more surprisingly, there are quite a few papers which address them. Here is a small sampler, in random order:. The reason I started collecting these links is kind of interesting.

Thus the links on my website. I recommend others also do this, as a navigational tool. Well, looks like none of my conjectures have been disproved yet. There has been a great deal of work on this problem, see e. Now, I was thinking about the case of the symmetric group trying to apply arithmetic combinatorics ideas and going nowhere.

Now, strictly speaking that judgement was correct, but much too gloomy. To my embarrassment, they referenced my slides as a validation of the importance of their work. In fact, it is possible that the diameter is always O n 2. We just have no idea. For simple groups of Lie type or large rank the existing worst case diameter bounds are exponential and much too weak compared to the desired bound.

He and coauthors proved the conjecture is some special cases, but it was wide open in full generality. Now, I thought about this type of problems before and was very skeptical. I spent a few days working on the problem to see if any of my tools can disprove it, and failed miserably.

But in my stubbornness I remained negative and suggested to Alejandro that he should drop the problem, or at least stop trying to prove rather than disprove the conjecture. I was wrong to do that. Luckily, Alejandro ignored my suggestion and soon after proved the polynomial part of the conjecture together with Joel Lewis. Their proof is quite elegant and uses certain recurrences coming from the rook theory.

These recurrences also allow a fast computation of these polynomials. Consequently, the authors made a number of computer experiments and disproved the positivity of coefficients part of the conjecture. So the moral is not to be so negative. Sometimes you need to prove a positive result first before moving to the dark side. Now, Itai Benjamini is a fantastic conjecture maker of the best kind, whose conjectures are both insightful and well motivated. While I always believed in that conjecture and even proved a tiny special case of it, finite versions tend to be much harder in my experience.

In any event, I thought a bit about the Benjamini conjecture and talked to Itai about it. He convinced me to work on it. Together with Chis Malon, we wrote a paper proving the claim for some Cayley graphs of abelian and some more general classes of groups. Despite our best efforts, we could not prove the conjecture even for Cayley graphs of abelian groups in full generality. Benjamini noted that the conjecture is tight for products of two cyclic groups, but that justification did not sit well with me.

There seemed to be no obvious way to prove the conjecture even for the Cayley graph of S n generated by a transposition and a long cycle, despite the very small O n 2 diameter. As it turns out, it was us who were being overly pessimistic, even if we never actually stated that we believe the conjecture is false.

Most recently, in an amazing development, Tom Hutchcroft and Matthew Tointon proved a slightly weaker version of the conjecture by adapting the methods of Duminil-Copin et al. They also extend our approach with Malon to prove the conjecture for all Cayley graphs of abelian groups. So while the Benjamini conjecture is not completely resolved, my objections to it are no longer valid. All in all, it looks like I was never formally wrong even if I was a little dour occasionally Yay!?

Turns out, some conjectures are actually true or at least likely to hold. While I continue to maintain that not enough effort is spent on trying to disprove the conjectures, it is very exciting when they are proved. I just finished my very first book review for the Notices of the AMS. The authors are Ezra Brown and Richard Guy , and the book title is the same as the blog post.

I had mixed feelings when I accepted the assignment to write this. I knew this would take a lot of work I was wrong — it took a huge amount of work. Here is how the book begins:. One reason why Combinatorics has been slow to become accepted as part of mainstream Mathematics is the common belief that it consists of a bag of isolated tricks, a number of areas: [very long list — IP] with little or no connection between them.

We shall see that they have numerous threads weaving them together into a beautifully patterned tapestry. Having read the book, I continue to maintain that there is no unity. Here is the first paragraph of the portion of the review where I touch upon themes very familiar to readers of this blog:. This attitude was unfair but reasonably common back in , outright insulting and relatively uncommon in , and was utterly preposterous in To finish this line of thought, it gives me no pleasure to conclude that the case for the unity of combinatorics is too weak to be taken seriously.

On the other hand, this lack of unity is not necessarily a bad thing, as we would be amiss without the rich diversity of cultures, languages, open problems, tools and applications of different areas. Enjoy the full review!

A large part of the book is freely downloadable. I made this website for the curious reader. I was not aware of the video until now. Watch the whole talk. You can now see three! Abel laureates discussing Combinatorics — follow the links in this blog post from Readers of this blog will remember my strong advocacy for taking interviews. Here is that interview. I am looking forward to read interviews of many more people in ECA and other journals.

The interview asks also about this blog, so it seems fitting to mention it here. Corrections: March 11, 1. Ugh, to the original question — none of my results would go on that list. Sorry everyone for all the confusion! The paper is not up on their website yet, but I already submitted the proofs. I admit that it takes a bit of a chutzpah to teach people how to write, so take it as you will. It is again aimed at a novice writer. There is a major difference between the way fiction is written vs.

To give you some flavor, here is a quote:. What kind of a story? Imagine a non-technical and non-detailed version of the abstract of your paper. It should be short, to the point, and straightforward enough to be a tweet , yet interesting enough for one person to want to tell it, and for the listener curious enough to be asking for details. Sounds difficult if not impossible? You are probably thinking that way, because distilled products always lack flavor compared to the real thing.

I hear you, but let me give you some examples. But there are enough hints to make some readers curious to look up the full story. The story here is spoiler alert! But you see my point — this story is a bit like an extended tag line, yet interesting enough to be discussed even if you know the ending.

You must be logged in to post a comment. Igor Pak's blog Views on life and math. Home About Igor Pak. Are we united in anything? February 10, igorpak 5 comments. Well, ok, good to know… Closer to home, you see the same themes said about the International Congress of Mathematicians to be held in St. What exactly unites us? Sounds reasonable until you actually think about what is being said… Even the style of doing research is completely different. Some are sort of in favor: I still believe the Olympics contribute a net benefit to humanity.

Some are blunt: More and more, the international spectacle has become synonymous with overspending, corruption, and autocratic regimes. The only highly controversial criticism that I found was from Ulf Persson who starts with : The congresses are by now considered to be monstrous affairs very different from the original intimate gatherings where group pictures could be taken.

This is what the view is like: Note that the ICM is not like a sports event — there is literally nothing at stake. And while I disagree with other things in the article below, I do agree with this basic premise: Totalitarian countries have unity. The insidious corruption of open access publishers January 9, igorpak 2 comments.

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In fact, this is a disservice to both the students and the area. Different students want to know about different aspects of Combinatorics. Thus, if you are teaching the same numbered undergraduate course every semester you can just split it into two or three, and fix different syllabi in advance. The students will sort themselves out and chose courses they are most interested in. They are broader, in fact, than the titles suggest — see Math and Math here.

The former turned out to be quite a bit more popular among many applied math and non-math majors, especially those interested in CS, engineering, data science, etc. Math majors tend to know a lot of this material and flock to the latter course. I am not saying you should do the same — this is just an example of what can be done. We now use both at UCLA. There are also many good Graph Theory course textbooks of all levels, of course. Similarly, for graduate courses, make sure you make the subject relatively narrow and clearly defined.

Like a topics class, except accessible to beginning graduate students. Low entry barrier is an advantage Combinatorics has over other areas, so use it. To give examples from my own teaching, see unedited notes from my graduate courses:. Combinatorics of posets Fall Combinatorics and Probability on groups Spring Algebraic Combinatorics Winter Discrete and Polyhedral Geometry Fall This is based on my book. See also videos of selected topics in Russian.

Combinatorics of Integer Sequences Fall Combinatorics of Words Fall Tilings Winter , lecture-by-lecture refs only. In my experience, the more specific you make the combinatorics course the more interesting it is to the students. You create a good course and the students will quickly figure it out.

They do have their own FB and other chat groups, and spread the news much faster than you could imagine…. Unfortunately, there is often no good textbook to cover what you want. So you might have to work a little harder harder to scout the material from papers, monographs, etc. In the internet era this is easier than ever. In fact, many extensive lecture notes are already available on the web.

Eventually, all the appropriate textbooks will be written. As I mentioned before , this is one of the very few silver linings of the pandemic…. Having said that, these voluminous textbooks can be incredibly valuable to both the students and the instructor as a source of interesting supplementary material. The enormity of the university administration can instill fear. How can you possibly fight such a machine?

Even if an injustice happened to you, you are just one person with no power, right? Well, I think you can. Whether you succeed in your fight is another matter. But at least you can try… In this post I will try to give you some advise on how to do this. Wait for future blog posts otherwise….

Warning : Much of what I say is relevant to big state universities in the US. Who am I to write about this? It is reasonable to ask if any of this is based on my personal experience of fighting university bureaucracies. The answer is yes, but I am not willing to make any public disclosures to protect privacy of all parties involved. Let me just say that over the past 20 years I had several relatively quiet and fairly minor fights with university bureaucracies some of which I won rather quickly by being right.

Once, I bullied my way into victory despite being in the wrong as I later learned , and once I won over a difficult non-personal political issue by being cunning and playing a really long game that took almost 3 years. By contrast, when I tried to fight the federal government a couple of times on academic matters , I lost quickly and decisively.

They are just too powerful…. Should you fight? But probably not. Say, you complained to the administration about what you perceive to be an injustice to you or to someone else. Your complaint was denied. This is when you need to decide if you want to start a fight. If you do, you will spend a lot of effort and on average probably lose. The administrations are powerful and know what they are doing. Can you fight? Yes, you can. You can win by being right and convince bureaucrats to see it this way.

You can win by being persistent when others give up. You can also win by being smart. Big systems have weaknesses you can exploit, see below. Use them. Is there a downside to winning a fight? In the process you might lose some friends, raise some suspicions from colleagues, and invite retribution.

On a positive side, big systems have very little institutional memory — your win and the resulting embarrassment to administration will be forgotten soon enough. Is there an upside to losing a fight? Actually, yes. You might gain resect of some colleagues as someone willing to fight.

And if your cause is righteous, this might help your reputation in and beyond the department. Why did I fight? The injustice, as I perceived it, was eating me alive and I had a hunch there is a nonzero chance I would win. There were cases when the issue was much too minor to waste my energy. Is there a cost of not fighting?

Yes, and it goes beyond the obvious. First , fighting bureaucracy is a skill, and every skill takes practice. I remember when tried to rent an apartment in Cambridge, MA — some real estate agents would immediately ask if I go to Harvard Law School. Most of these lawsuits would quickly fail, but the legal proceeding were costly to the owners.

Second , there is a society cost. If you feel confident that your case is strong, you winning might set a precedent which could benefit many others. Know your adversary. Remember — you are not fighting a mafia, a corrupt regime or the whole society. Your adversary is a group of good people who are doing their jobs as well as they can. They are not infallible, but probably pretty smart and very capable when it comes to bureaucracy, so from game theory point of view you may as well assume they are perfect.

Know your rights. This might seem obvious, but you would be surprised to know how many academics are not aware they have rights in a university system. For example, Wikipedia is a large project which survived for 20 years, so unsurprisingly it has a large set of policies enforced by an army of admins. The same is probably true about your university and your department. Search on the web for the faculty handbook, university and department bylaws, etc.

Go through the motions. Say, you think you were slighted. Whatever it is, you are upset, I get it. Your first step is not to complain but go through the motions, and email inquiries. Email the head of the department, chair of the executive committee, your faculty dean, etc. Calmly ask to explain this decision. You win, case closed. Also, sometimes you either get a convincing explanation with which you might agree — say, the university is on salary freeze so nobody got a salary increase, see some link.

Again, case closed. These are the cases that you need to know how to handle and all such cases are a little different. I will try to cover as much territory as possible, but surely will miss some cases. Ask for advice. This is especially important if you are a junior mathematician and feel a little overwhelmed.

Find a former department chair, perhaps professor emeritus, and have an quiet chat. They might also suggest who else you should talk to that would be knowledgeable and help dealing with an issue. With friends like these, you are in a good shape. Come by for a chat. This is a standard move by a capable bureaucrat. You lost. There is only one way to counter this move.

Agree to a meeting — play nice and you might learn something. This defeats the purpose of the meeting moving you back to square one. At the meeting do not agree with anything, never say yes or no to anything. Do not sign anything. If offered a document to sign, take it with you. Get it all in writing. Within a few hours after the meeting, email to the bureaucrat an email with your notes.

I am writing this to ensure there is no misunderstanding on my part. A capable bureaucrat will recognize the move and will never go on record with anything unbecoming. They will accept the out you offered and claim that you indeed misunderstood. In lieu of the misunderstanding they will need to give a real answer to your grievance otherwise what was the point of the meeting? Sometimes a bureaucrat will still resort to platitudes, but now that they are in writing, that trick is harder to pull off, and it leads us to a completely different scenario see below.

Accept the win. If not, follow up about details. Accept the defeat. Remain calm. Power of CC. If you receive a non-answer full of platitudes or no email reply at all give it exactly one week , then follow up. I would really appreciate your response to [all issues I raised].

Most likely you will get a reply within hours. This is extremely atypical and related to [your unusual circumstances]. While this is normally not appropriate, we are happy to make an exception in your case and [compensate you].

Now, there is only one way to counter this, as far as I know. The only way out is to pretend to be just as illogical as the bureaucrat pretends to be. I gratefully accept your sincere apology and your assurances this will not happen again to me nor anyone else at the department. A capable bureaucrat will recognize they are fighting fire with fire.

Now that seem overly defensive. And they would have to reply to the whole CC list again, which is not what they want. They are aware that everyone else knows they screwed up, so reminding everyone with a new email is not in their interest. And there is a decent chance you might reply to the whole CC list again with all that sugarcoated unpleasantness.

Shifting blame or responsibility. This is great news for you — a tacit validation of your cause and an example of a bureaucrat putting their own well-being ahead of the institution. Remember, your fight is not with X, but with the administration. Like with musical chairs, you might have to repeat the procedure a few times, but chances are someone will eventually accept responsibility just to stop this embarrassment from going circles.

By then, there will be so many people on the CC chain, your issue will be addressed appropriately. Help them help you. Sometimes a complaint puts the bureaucrat into a stalemate. They want to admit that injustice happened to you, but numerous university rules forbid them from acting to redress the situation. In order to violate these rules, they would have to take the case upstairs, which brings its own complications to everyone involved.

Essentially you need to throw them a lifeline by suggesting some creative solution to the problem. While the bureaucrat may not agree with your proposed solution, your willingness to deal without an apology will earn you some points and perhaps lead to a resolution favorable to all parties. It is a common misconception that university administrations are very slow and rigid.

In reality, when they want to, such large systems can turn on a dime by quickly utilizing its numerous resources human, financial, legal, etc. Making it public. Just about every time you make grievances public you lose some social points with people who will hold it against you, claim you brought it on yourself, etc. In the world of social media your voice will be drowned and your case will be either ignored or take life of its own, with facts distorted to fit a particular narrative.

The administration will close ranks and refuse to comment. You might be worse off than when you started. The only example I can give is my own combative blog post which remains by far my most widely read post. Everyone just loves watching a train wreck… Many people asked why I wrote it, since it made me a persona non grata in the whole area of mathematics. There is really nothing I can do and they know it. But you can very indirectly threaten to make it public.

Low level university bureaucrats are not really afraid for their jobs. For example, head of the department might not even want to occupy the position, and is fully protected by tenure anyway. But deans, provosts, etc.

In this case I recommend you find an email of some student editor of a local university newspaper. I am confident there will be people on all sides who disagree collectively with just about every sentence I wrote. Remember — this blog post is a not a recommendation to do anything.

Good luck everyone! Hope you will never have to deal with any of that! In our math research we make countless choices. We chose a problem to work on, decide whether its claim is true or false, what tools to use, what earlier papers to study which might prove useful, who to collaborate with, which computer experiments might be helpful, etc. Choices, choices, choices… Most our choices are private. Others are public. This blog is about wrong public choices that I made misjudging some conjectures by being overly pessimistic.

As I have written before , conjectures are crucial to the developments of mathematics and to my own work in particular. The concept itself is difficult, however. To understand this, note the stark contrast with experimental physics, as many mathematical conjectures are not particularly testable yet remain quite interesting.

For example, if someone conjectures there are infinitely many Fermat primes , the only way to dissuade such person is to actually disprove the claim. There is also an important social aspect of conjecture making. For a person who poses a conjecture, there is a certain clairvoyance respected by other people in the area.

Predictions are never easy , especially of a precise technical nature, so some bravery or self-assuredness is required. Note that social capital is spent every time a conjecture is posed. Now, for the person working on a conjecture, there is also a betting aspect one cannot ignore. As in, are you sure you are working in the right direction? The success in solving a well known conjecture is often regarded much higher than a comparable result nobody asked about.

This may seem unfair, and there is a bit of celebrity culture here. Thinks about it this way — two lead actors can have similar acting skills, but the one who is a star will usually attract a much larger audience…. Not unlike what happens to papers and mathematical results , conjectures also have stories worth telling, even if these stories are rarely discussed at length. Let me list a few scenarios, from the least to the most mathematically helpful:.

Say, you are working on a major open problem. You realize that a famous conjecture A follows from a combination of three conjectures B , C and D whose sole motivation is their applications to A. Some of these smaller conjectures are beyond the existing technology in the area and cannot be checked computationally beyond a few special cases.

Somebody points out that D is trivially false. Everyone else shrugs and moves on. You are working in a major field of study aiming to prove a famous open problem A. Over the years you proved a number of special cases of A and became one the leaders of the area. You are very optimistic about A discussing it in numerous talks and papers. Suddenly A is disproved in some esoteric situations, undermining the motivation of much of your older and ongoing work. In your ongoing work you stumble at a coincidence.

You are clueless why would that be true, since being nice belongs to another area X. Being nice is also too abstract to be checked easily on a computer. So you mention it in the Final Remarks section of your latest paper in vain hope somebody reads it. You are doing computer experiments related to your work.

Suddenly certain numbers appear to have an unexpectedly nice formula or a generating function. You check with OEIS and the sequence is there indeed, but not with the meaning you wanted. You think deeply about famous conjecture A. Not only your realize that there is no way one can approach A in full generality, but also that it contradicts some intuition you have about the area. However, A was stated by a very influential person N and many people believe in A proving it in a number of small special cases.

You want to state a non-A conjecture, but realize the inevitable PR disaster of people directly comparing you to N. You think deeply about the area and realize that there is a fundamental principle underlying certain structures in your work. Formalizing this principle requires a great deal of effort and results in a conjecture A. Obviously, there are many other possible stories, while some stories are are a mixture of several of these. Turns out, over the years I made a lot of those. Even more surprisingly, there are quite a few papers which address them.

Here is a small sampler, in random order:. The reason I started collecting these links is kind of interesting. Thus the links on my website. I recommend others also do this, as a navigational tool. Well, looks like none of my conjectures have been disproved yet. There has been a great deal of work on this problem, see e. Now, I was thinking about the case of the symmetric group trying to apply arithmetic combinatorics ideas and going nowhere.

Now, strictly speaking that judgement was correct, but much too gloomy. To my embarrassment, they referenced my slides as a validation of the importance of their work. In fact, it is possible that the diameter is always O n 2. We just have no idea. For simple groups of Lie type or large rank the existing worst case diameter bounds are exponential and much too weak compared to the desired bound.

He and coauthors proved the conjecture is some special cases, but it was wide open in full generality. Now, I thought about this type of problems before and was very skeptical. I spent a few days working on the problem to see if any of my tools can disprove it, and failed miserably. But in my stubbornness I remained negative and suggested to Alejandro that he should drop the problem, or at least stop trying to prove rather than disprove the conjecture.

I was wrong to do that. Luckily, Alejandro ignored my suggestion and soon after proved the polynomial part of the conjecture together with Joel Lewis. Their proof is quite elegant and uses certain recurrences coming from the rook theory. These recurrences also allow a fast computation of these polynomials. Consequently, the authors made a number of computer experiments and disproved the positivity of coefficients part of the conjecture.

So the moral is not to be so negative. Sometimes you need to prove a positive result first before moving to the dark side. Now, Itai Benjamini is a fantastic conjecture maker of the best kind, whose conjectures are both insightful and well motivated. While I always believed in that conjecture and even proved a tiny special case of it, finite versions tend to be much harder in my experience.

In any event, I thought a bit about the Benjamini conjecture and talked to Itai about it. He convinced me to work on it. Together with Chis Malon, we wrote a paper proving the claim for some Cayley graphs of abelian and some more general classes of groups.

Despite our best efforts, we could not prove the conjecture even for Cayley graphs of abelian groups in full generality. Benjamini noted that the conjecture is tight for products of two cyclic groups, but that justification did not sit well with me. There seemed to be no obvious way to prove the conjecture even for the Cayley graph of S n generated by a transposition and a long cycle, despite the very small O n 2 diameter.

As it turns out, it was us who were being overly pessimistic, even if we never actually stated that we believe the conjecture is false. Most recently, in an amazing development, Tom Hutchcroft and Matthew Tointon proved a slightly weaker version of the conjecture by adapting the methods of Duminil-Copin et al. They also extend our approach with Malon to prove the conjecture for all Cayley graphs of abelian groups.

So while the Benjamini conjecture is not completely resolved, my objections to it are no longer valid. All in all, it looks like I was never formally wrong even if I was a little dour occasionally Yay!? Turns out, some conjectures are actually true or at least likely to hold. While I continue to maintain that not enough effort is spent on trying to disprove the conjectures, it is very exciting when they are proved. I just finished my very first book review for the Notices of the AMS.

The authors are Ezra Brown and Richard Guy , and the book title is the same as the blog post. I had mixed feelings when I accepted the assignment to write this. I knew this would take a lot of work I was wrong — it took a huge amount of work. Here is how the book begins:. One reason why Combinatorics has been slow to become accepted as part of mainstream Mathematics is the common belief that it consists of a bag of isolated tricks, a number of areas: [very long list — IP] with little or no connection between them.

We shall see that they have numerous threads weaving them together into a beautifully patterned tapestry. Having read the book, I continue to maintain that there is no unity. Here is the first paragraph of the portion of the review where I touch upon themes very familiar to readers of this blog:. This attitude was unfair but reasonably common back in , outright insulting and relatively uncommon in , and was utterly preposterous in To finish this line of thought, it gives me no pleasure to conclude that the case for the unity of combinatorics is too weak to be taken seriously.

On the other hand, this lack of unity is not necessarily a bad thing, as we would be amiss without the rich diversity of cultures, languages, open problems, tools and applications of different areas. Enjoy the full review! A large part of the book is freely downloadable. I made this website for the curious reader.

I was not aware of the video until now. Watch the whole talk. You can now see three! Abel laureates discussing Combinatorics — follow the links in this blog post from Readers of this blog will remember my strong advocacy for taking interviews. Here is that interview.

I am looking forward to read interviews of many more people in ECA and other journals. The interview asks also about this blog, so it seems fitting to mention it here. Corrections: March 11, 1. Ugh, to the original question — none of my results would go on that list. Sorry everyone for all the confusion! The paper is not up on their website yet, but I already submitted the proofs.

I admit that it takes a bit of a chutzpah to teach people how to write, so take it as you will. It is again aimed at a novice writer. There is a major difference between the way fiction is written vs. To give you some flavor, here is a quote:. What kind of a story? Imagine a non-technical and non-detailed version of the abstract of your paper. It should be short, to the point, and straightforward enough to be a tweet , yet interesting enough for one person to want to tell it, and for the listener curious enough to be asking for details.

Sounds difficult if not impossible? You are probably thinking that way, because distilled products always lack flavor compared to the real thing. I hear you, but let me give you some examples. But there are enough hints to make some readers curious to look up the full story. The story here is spoiler alert! But you see my point — this story is a bit like an extended tag line, yet interesting enough to be discussed even if you know the ending.

You must be logged in to post a comment. Igor Pak's blog Views on life and math. Home About Igor Pak. Are we united in anything? February 10, igorpak 5 comments. Well, ok, good to know… Closer to home, you see the same themes said about the International Congress of Mathematicians to be held in St.

What exactly unites us? Sounds reasonable until you actually think about what is being said… Even the style of doing research is completely different. Some are sort of in favor: I still believe the Olympics contribute a net benefit to humanity. Some are blunt: More and more, the international spectacle has become synonymous with overspending, corruption, and autocratic regimes.

The only highly controversial criticism that I found was from Ulf Persson who starts with : The congresses are by now considered to be monstrous affairs very different from the original intimate gatherings where group pictures could be taken. This is what the view is like: Note that the ICM is not like a sports event — there is literally nothing at stake.

And while I disagree with other things in the article below, I do agree with this basic premise: Totalitarian countries have unity. The insidious corruption of open access publishers January 9, igorpak 2 comments. What is MDPI? See also this response by MDPI. What is Mathematics? Uhm… So, who are these people? Slim pickings for someone who knows thousands of mathematicians… This journal is popular, seriously? The reasons for popularity are also transparent: they accept all kinds of nonsense.

Now try explaining to the editor why your old weaker paper should be published in favor of all this new shining stuff… This is yet another place where MDPI is innovative. What makes MDPI special? How do you tell they are illegitimate then? What exactly does the Mathematics do? Ugh… 3 They spam junior researchers asking them to submit to their numerous special issues, and in return to accept their publishing model.

One author reported that the journal made them write a sentence The first part of the bibliography […], numbered in chronological order from [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,,….

What gives? What happens to math journal in the future? The symbolism In American universities, the antisemitism was widespread practice for decades which went out of fashion along with slide rule and French curve. And now this Consider the present day case of Yaroslav Shitov which was pointed out to me last week. The problem with combinatorics textbooks July 3, igorpak Leave a comment. Courses and textbooks How should one resolve the issue raised above? To give examples from my own teaching, see unedited notes from my graduate courses: Combinatorics of posets Fall Combinatorics and Probability on groups Spring Algebraic Combinatorics Winter Discrete and Polyhedral Geometry Fall This is based on my book.

Combinatorics of Integer Sequences Fall Combinatorics of Words Fall Tilings Winter , lecture-by-lecture refs only In summary In my experience, the more specific you make the combinatorics course the more interesting it is to the students. They do have their own FB and other chat groups, and spread the news much faster than you could imagine… Unfortunately, there is often no good textbook to cover what you want. As I mentioned before , this is one of the very few silver linings of the pandemic… P.

How to fight the university bureaucracy and survive June 27, igorpak Leave a comment. Wait for future blog posts otherwise… Warning : Much of what I say is relevant to big state universities in the US. Basics Who am I to write about this? Besides, the website design is very nice too. Everything is simple and comprehensible.

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