Today is the general election day in Israel, the third since starting this blog (I-2009,and II-2013). This is an exciting day. For me election is about participation much more than it is about influence and I try not to miss it. This time, for the first time, I publicly supported one political party “the Zionist camp” headed by Herzog and Livni. The last four posts written in Hebrew are related to my position. (The fourth one has a poll which expresses also some academic curiosity, and I plan one more post with a similar follow-up but post-election poll. But then we go back to combinatorics and more)

The blog also has now a new appearance and the header is a picture from 1999 with Jirka Matousek, a great mathematician and a great person who enlightened our community and our lives in many ways and who passed away at a terribly young age last Tuesday.

זו הפעם החמש-עשרה שבה אצביע והפעם השלישית שאנו נמצאים לפני בחירות מאז שהתחלתי בכתיבת הבלוג. בעבר לא הבעתי בפומבי את הבחירה האישית שלי. עבורי יום הבחירות הוא יום חג, ההכרעות בין תפיסות עולם ואינטרסים מנוגדים אינן קלות, ויש דרכים שונות, אותן אני מכבד, לשפוט את המציאות ואת המתמודדים

זו הפעם הראשונה שאני נותן ביטוי פומבי לבחירתי

כתמיד כל ממשלה שתוקם לאחר הבחירות תצטרך להתמודד עם קשיים, איומים
ואולי אף עם מלחמות, אבל הפעם, ללא שינוי בהנהגת המדינה, אני רואה אפשרות קשה להתדרדרות של ערכי יסוד של החברה שלנו ביחד עם התדרדרות והשחתה של מערכות המדינה והחברה

The topological Tverberg conjecture (discussed in this post), a holy grail of topological combinatorics, was refuted! The three-page paper “Counterexamples to the topological Tverberg conjecture” by Florian Frick gives a brilliant proof that the conjecture is false.

The proof is based on two major ingredients. The first is a recent major theory by Issak Mabillard and Uli Wagner which extends fundamental theorems from classical obstruction theory for embeddability to an obstruction theory for r-fold intersection of disjoint faces in maps from simplicial complexes to Euclidean spaces. An extended abstract of this work is Eliminating Tverberg points, I. An analogue of the Whitney trick. The second is a result by Murad Özaydin’s from his 1987 paper Equivariant maps for the symmetric group, which showed that for the non prime-power case the topological obstruction vanishes.

It was commonly believed that the topological Tverberg conjecture is correct. However, one of the motivations of Mabillard and Wagner for studying elimination of higher order intersection was that this may lead to counterexamples via Özaydin result. Isaak and Uli came close but there was a crucial assumption of large codimension in their theory, which seemed to avoid applying the new theory to this case. It turned out that a simple combinatorial argument allows to overcome the codimension problem!

Florian’s combinatorial argument which allows to use Özaydin’s result in Mabillard-Wagner’s theory is a beautiful example of a powerful combinatorial method with other applications by Pavle Blagojević, Florian Frick and Günter Ziegler.

Both Uli and Florian talked about it here at Oberwolfach on Tuesday. I hope to share some more news items from Oberwolfach and from last week’s Midrasha in future posts.

Update 3 (January 30): The midrasha ended today. Update 2 (January 28): additional videos are linked; Update 1 (January 23): Today we end the first week of the school. David Streurer and Peter Keevash completed their series of lectures and Alex Postnikov started his series.

___

Today is the third day of our winter school. In this page I will gradually give links to to various lectures and background materials. I am going to update the page through the two weeks of the Midrasha. Here is the web page of the midrasha, and here is the program. I will also present the posters for those who want me to: simply take a picture (or more than one) of the poster and send me. And also – links to additional materials, pictures, or anything else: just email me, or add a comment to this post.

Scott Aaronson wrote a new post on the Shtetl Optimized** reflecting on the previous thread (that I referred to in my post on Amy’s triumph), and on reactions to this thread. The highlight is a list of nine of Scott’s core beliefs. This is a remarkable document and I urge everybody to read it. Yes, Scott’s core beliefs come across as feminist! Let me quote one of them.

7. I believe that no one should be ashamed of inborn sexual desires: not straight men, not straight women, not gays, not lesbians, not even pedophiles (though in the last case, there might really be no moral solution other than a lifetime of unfulfilled longing). Indeed, I’ve always felt a special kinship with gays and lesbians, precisely because the sense of having to hide from the world, of being hissed at for a sexual makeup that you never chose, is one that I can relate to on a visceral level. This is one reason why I’ve staunchly supported gay marriage since adolescence, when it was still radical. It’s also why the tragedy of Alan Turing, of his court-ordered chemical castration and subsequent suicide, was one of the formative influences of my life.

!! (***)

In the sacred tradition of arguing with Scott I raised some issues with #5 and 4# on Scott’s blog. Two of Scott’s points are on the subject of (young) people’s suffering by feeling unwanted, sexually invisible, or ashamed to express their desires.

I was pleased to see that those feminist matters that Scott and I disagree about, like the nature of prostitution, the role of feminist views in men’s (or nerdy men’s) suffering, and also Scott’s take on poverty, did not make it to Scott’s core beliefs.

Happy new year, everybody!

* The word triumph is used here (again) in a soft (non-macho) way characteristic to the successes of feminism. Voting rights for women did not exclude voting rights for men, and Scott’s triumph does not mean a defeat for any others; on the contrary.

** “Shtetl-optimized” is the name of Scott Aaronson’s blog.

*** In my opinion, when a person has an uncontrollable urge or strong temptation or desire to commit a crime towards another individual (or even to inflict much damage on another person when it is not criminal, or to commit other crimes), shame and guilt feelings can be instrumental in controlling such urges.

Ilya Rips and me during Ilyafest last week (picture Itai Benjamini)

Ilya Rips Birthday Conference

Last week we had here a celebration for Ilya Rips’ birthday. Ilya is an extraordinary mathematician with immense influence on algebra and topology. There were several startling ongoing mathematical projects that he is involved with that were discussed. One is a very ambitious project with Alexei Kanel-Belov is to get a “small cancellation theory” for rings and this has already fantastic consequences. Another is a work with Yoav Segev and Katrin Tent, on sharply 2- transitive groups, that answered a major old question with connections to groups, rings, and geometry. Happy birthday, Ilya!

Achimedes on infinity

Reviel Netz (רויאל נץ) gave a seminar lecture in the department about infinity in Archimedes’ mathematical thoughts that developed into an interesting conversation. The lecture took place a day after Netz’s second poetry book (in Hebrew) appeared.

The combinatorics school (midrasha) is coming.

Two weeks with extensive illuminating lecture series. Do not miss!

At Combsem

On our Monday combinatorics seminar, we had, since my last report, three excellent lectures. And next Monday we are having Avi Wigderson.

Dec 1

Speaker: Sonia Balagopalan, HU

Title: A 16-vertex triangulation of the 4-dimensional real projective space