Date/Time : 19 Aug 2026 13:30
Venue : S16 #05-18
Speaker : Liron Speyer, Okinawa Institute of Science and Technology

I will give a brief account of the combinatorial representation theory of type A Iwahori–Hecke algebras, and their realisation as cyclotomic KLR algebras. In this story, I will largely focus on the decomposition number problem as one of the key problems in this field, and James’s conjecture, which drove a lot of research until Williamson showed it to be false in 2013. While Williamson’s counterexample is incredibly large, and beyond explicit computation, I recently discovered a new counterexample, which is of minimal size. I will explain this counterexample in the talk, as well as touching on how I found it.

Add to calendar :

Date/Time : 19 Aug 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Clement Yung, University of Toronto

In the past century, the insight behind the original Ramsey’s theorem proved to be applicable to a wide range of mathematics, such as number theory, functional analysis and topology. This spurred two particular directions of Ramsey theory: The first one is known as topological Ramsey theory, a general procedure developed by Carlson and Simpson to prove many seemingly unrelated Ramsey’s theorem-like results. The second one is the Ramsey theory of Banach spaces, kickstarted by Gowers’ unexpected application of Ramsey theory to resolve a long-standing open problem in Banach space theory. In this talk, I introduce the theory of weak A2 spaces, which serves as a possible intersection between these two Ramsey theories and discuss how several infinite games that appeared in these Ramsey theories (the Kastanas game, the Gowers game and the asymptotic game) are closely related.

Add to calendar :

Date/Time : 17 Aug 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Katsuyuki Bando, Keio University

The geometric Satake equivalence is the categorification of the Satake isomorphism. Its derived version, “the derived geometric Satake equivalence,” is proved by Bezrukavnikov-Finkelberg in the case of equal characteristic. In this talk, we will explain a new affine Grassmannian which connects an equal characteristic affine Grassmannian and Zhu’s Witt-vector affine Grassmannian. As a result, we deduce the derived Satake equivalence in mixed characteristic. By the same argument, we also obtain the mixed characteristic version of Bezrukavnikov’s equivalence between two categorifications of an affine Hecke algebra. Moreover, we explain the derived geometric Satake equivalence on the Beilinson–Drinfeld Grassmannian with one leg in mixed characteristic.

Add to calendar :

Date/Time : 17 Aug 2026 11:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : In-Jee Jeong, Korea Institute For Advanced Study

For the incompressible Euler equation in vorticity form in two and three dimensions, we consider the initial value problem with data in the critical Sobolev space, W^{d/p,p}(R^d). In the case 1<p<infinity, we give a simple proof of strong illposedness, based on the Hardy inequality and “Key Lemma” of Kiselev and Sverak, using vorticities having the form of “diadic bubbles”. Then, we discuss endpoint cases, namely p = 1 and p = infinity.

Add to calendar :

Date/Time : 13 Aug 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Boaz Klartag, Tel Aviv University and Weizmann Institute of Science

We survey progress from the past five years on the distribution of mass in high-dimensional convex bodies and in probability distributions with convexity properties. The concentration of measure phenomenon has traditionally been studied in highly regular or structured settings, such as spheres, Hamming cubes, Gaussian measures, Markov chains, and martingales. It turns out that convexity assumptions provide an alternative source of regularity in high dimensions with remarkably similar features: Lipschitz functions are highly concentrated, the isoperimetric problem is nearly saturated by half-spaces (up to logarithmic factors), and the central limit theorem is nearly as strong as in the setting of independent random variables. The main developments discussed include the resolution of Bourgain’s slicing problem and the Variance Conjecture, as well as recent progress on the isoperimetric problem for high-dimensional convex bodies. Based on joint work with P. Bizeul and J. Lehec.

Add to calendar :

Date/Time : 12 Aug 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Wenfei Liu, Xiamen University

The set V of volumes of stable surfaces, as a subset of positive rational numbers, satisfies the descending chain condition. Equivalently, any nonempty subset of V attains the minimum.

In this talk, I will report a joint work with Jihao Liu, showing that the minimal volume of a stable surface with Picard rank 1 is 1/6351, uniquely realized by a normal rational stable surface previously constructed from P^2 with 4 lines by Valery Alexeev and Wenfei Liu.

In the proof of the minimum, we use various filters to narrow down the possible basket of singularities on such a surface.

The last and very crucial one, the so-called pluricanonical product-dimension filter, was suggested to us by the AI!

Add to calendar :

Date/Time : 12 Aug 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Boaz Klartag, Tel Aviv University and Weizmann Institute of Science

We prove there exists a lattice sphere packing in R^n whose density is at least c n^2 / 2^n, where c > 0 is a universal constant. Previously known constructions of sphere packings in R^n had densities of the order of magnitude of n / 2^n, up to logarithmic factors. Our proof utilizes a stochastically evolving ellipsoid that accumulates at least c n^2 lattice points on its boundary, while containing no lattice points in its interior except for the origin.

Add to calendar :

Date/Time : 12 Aug 2026 13:30
Venue : S16 #05-18
Speaker : Dinesh S. Thakur, University of Rochester

After reviewing some basic facts of classical diophantine approximation, diophantine equations, we will discuss various analogs, contrasts, tools, and open questions in the finite characteristic situation.

Add to calendar :

Date/Time : 12 Aug 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Wang Wei, Sun Yat-Sen University

A (binary) tree is positive iff its infinite paths form a set with positive Lebesgue measure. It is a well-known phenomenon in algorithmic randomness that positive trees contain infinite paths with weak computational power. By Cantor, positive trees always have perfect subtrees and even positive perfect subtrees. Chong et al. [1] studied computational power of perfect subtrees of positive trees, and to some extend showed that positive trees also contain perfect subtrees of weak computational power. This work was followed up by Barmpalias and Wang [2], by Barmpalias and Zhang [3], and also by Greenberg, J. Miller and Nies [4]. This talk will survey the main results in the above works, and also sketch a recent result that every ∆n positive tree contains a lown perfect subtree.

[1] Chong, Chitat and Li, Wei and Wang, Wei and Yang, Yue, On the com-putability of perfect subsets of sets with positive measure, Proceedings of the Amer-ican Mathematical Society, vol. 147 (2019), no. 9, pp. 4021–4028.
[2] Barmpalias, George and Wang, Wei, Pathwise-randomness and models of second-order arithmetic, Information and Computation, vol. 299 (2024), 105181.
[3] Barmpalias, George and Zhang, Xiaoyan, Growth and irreducibility in path-incompressible trees, Information and Computation, vol. 297 (2024), 105136.
[4] Greenberg, Noam and Miller, Joseph S. and Nies, André, Highness prop-erties close to PA completeness, Israel Journal of Mathematics, vol. 244 (2021), pp. 419–465.

Add to calendar :