Date/Time : 01 Dec 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Ichiro Shimada , Hiroshima University

The affine Conway group is the group of affine isometries of the Leech lattice. This group is isomorphic to the automorphism group of a standard fundamental domain for the action of the Weyl group on the even hyperbolic lattice of rank 26. The affine Conway group has exactly nine conjugacy classes of involutions. I explain their properties and show that, among these nine classes, one class can be regarded as an analogue of Enriques involutions of K3 surfaces.

Add to calendar :

Date/Time : 18 Nov 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Kenji Nakanishi, Kyoto University

Since the pioneering work of Kenig and Merle, there have been numerous results on global behavior of large general solutions to nonlinear dispersive equations that vary depending on the initial data, from asymptotically linear or scattering solutions to solitons and blow-up. The main question is to distinguish the types of solutions or to predict them from the initial data, without any asymptotic solution formula such as those provided by the inverse scattering theory in the special case of completely integrable systems. Despite of some spectacular progress such as the soliton resolution without size restriction, the range of applicable equations has been rather limited, such as the nonlinear wave equation or Schrodinger with simple nonlinearity, because certain monotonicity or invariance properties play crucial roles in the analysis without small factor. The Zakharov system is a model of the Langmuir turbulence in plasma, coupling the Schrodinger and the wave equations, and may be regarded also as a mathematical model to extend the methods from the simple scalar equations. It has been quite successful in the last decade for space dimensions 3 and 4, in spite of a few difficulties such as the derivative loss, the lower degree of nonlinear interactions, and the loss of invariance for scaling and for momentum or coordinate velocity. This talk will review the state of art, together with some detail on most recent results and open problems.

Add to calendar :

Date/Time : 28 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Ye Jinhe, University of Hong Kong

The classical inverse Galois problem asks whether every finite group occurs as a Galois group over ℚ. A geometric generalization is the regular inverse Galois problem over a field K, which asks for regular realizations over K(t). For K = ℚ, such realizations yield solutions to the classical problem by Hilbert irreducibility. While the regular inverse Galois problem remains open over ℚ, it is known to have a positive solution over large fields. In this talk, I will discuss a positive solution over curve-excluding fields, which are existentially closed among fields avoiding a fixed curve and provide a class of non-large fields over which the problem can be solved.

Add to calendar :

Date/Time : 28 Oct 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Kari Vilonen, University of Melbourne

I will explain recent joint work with Emerton and Davis. We formulate a conjecture which gives the cohomology of locally symmetric spaces as a cohomology of a coherent sheaf on the side of the Langlands parameters. The description is in terms of the categorical local Langlands. In particular, we explain the Archimedean contribution. We have verified the conjecture in large numbers of cases, for example, it gives the correct answer for the Eisenstein component.

Add to calendar :

Date/Time : 28 Oct 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Ting Xue, University of Melbourne

We explain a uniform construction of cuspidal character sheaves in the setting of Z/mZ-graded Lie algebras. We show that all cuspidal character sheaves arise from the Fourier-Sato transform of nearby cycle sheaves associated to very special supercuspidal data. These data essentially come from Lusztig’s cuspidal character sheaves on (ungraded) reductive Lie algebras. We discuss applications to affine Springer fibres via connection with Lusztig-Yun’s work, where double affine Hecke algebras enter the picture. This is based on joint work with Wille Liu, Cheng-Chiang Tsai and Kari Vilonen.

Add to calendar :

Date/Time : 28 Oct 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Guillaume Tahar, Guangdong Technion – Israel Institute of Technology

On a topological sphere endowed with a flat metric with conical singularities, the curvature gap quantifies the obstruction to realize a partition of the set of conical singularities into two sets of equal total angle defect. Unless its curvature gap is equal to zero, such a flat sphere cannot contain a simple closed geodesic. Drawing on the Delaunay decompositions of flat surfaces, we give a quantitative generalization of the latter statement. We prove that when the curvature gap is nonzero, there is an explicit upper bound on the lengths of simple geodesic trajectories in the flat sphere. If time allows, we will give extensions of this result to affine structures on punctured spheres and applications to dynamics of germs of biholomorphism tangent to the identity in complex dimension two. This is a work in collaboration with Xavier Buff, Arnaud Cheritat and Kai Fu.

Add to calendar :

Date/Time : 28 Oct 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Guillaume Tahar, Guangdong Technion – Israel Institute of Technology

The geodesic flow on the tangent bundle of a Riemann surface endowed with a complex affine structure (or, equivalently, a meromorphic connection) is a dynamical system that exhibits remarkable similarities with the real integral curves of polynomial vector fields in two variables and with the dynamics of germs of biholomorphisms tangent to the identity in complex dimension two. We will present the geometric interpretation of the singularities of the connection, including, time permitting, irregular singularities, and show that many geometric properties of an affine surface can be read from the topology of the bifurcation locus in its tangent bundle. We will also discuss applications to irrational triangular billiards and the classification of geodesic flows up to real affine and holomorphic conjugacy. This is joint work with Xavier Buff and Arnaud Chéritat.

Add to calendar :

Date/Time : 28 Oct 2026 15:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Matteo Carducci, Scuola Normale Superiore Pisa

In this talk, we discuss the question of uniqueness of blow-ups in the Alt-Phillips free boundary problem. After a brief introduction to the problem, we present our main results. These include uniqueness of blow-ups for a large class of Alt-Phillips cones, sharp rates of convergence to them, and explicit examples of cones, including a characterization of the minimality of the radial cone.

Add to calendar :

Date/Time : 21 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Nurlan Markhabatov, Eurasian National University (Astana, Kazakhstan)

This talk investigates model-theoretic properties of pseudofinite unars (where a unar is an algebra with a single unary operation). A criterion for the uncountable categoricity of pseudofinite unar theories is obtained. Examples of pseudofinite unar theories are constructed that are superstable but not ω-stable, ω-stable but not strongly minimal, and ω-stable but not uncountably categorical. It is also shown that the theory of every bounded unar is pseudofinite and ω-stable. During the talk, we will also attempt to formulate a general criterion for the pseudofiniteness of unars.

Add to calendar :