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.

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Date/Time : 30 Sep 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Jack Thorne, University of Cambridge

Although computing the set of solutions to a given Diophantine equation is hard (!), the solution sets of families of equations often display striking statistical regularity – this is the case, for example, for the family of Weierstrass elliptic curves over Q given by the equations y^2 = x^3+ Ax + B. For a randomly chosen curve in this family, one expects to see either no solutions or infinitely many solutions, each case occurring with probability 1/2. Striking results in this direction have been proved for these curves and for the hyperelliptic curves y2 = x^{2n+1} + … + c_{2n+1} in the Fields medal-winning work of Bhargava (with co-authors including Shankar and Gross).

One of the main ingredients in these works is a bridge between rational points and the space of lattices (i.e. discrete, cocompact subgroups in Euclidean space) — a Riemannian manifold of finite volume that plays a recurring role in number theory, and is familiar (in the rank 2 case) as the quotient of the upper half plane by the group SL(2, Z). I will survey this picture and describe recent work with Jef Laga, which shows that we can use this formalism to understand not only the number of rational points but their physical properties (e.g. their heights).

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Date/Time : 23 Sep 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Frank den Hollander, Leiden University

In this talk I present an overview of what is known and is not known about random processes on dynamic random graphs in co-evolution, i.e., with mutual feedback. The literature offers plenty of heuristics, simulations and conjectures, but so far mathematical results are extremely scarce. I describe some of these results, with a focus on opinion dynamics. In particular, I consider random graphs in which vertices can have one of two possible opinions. Pairs of vertices connected by an edge share their opinions according to a rate that may depend on the size of the graph. Each edge turns on or off according to a rate that depends on whether the vertices at its two endpoints have the same opinion or not. I exhibit joint evolution equations and describe the occurrence of phase transitions between consensus and polarisation.

Based on joint work with Siva Athreya (Bangalore) and Adrian Rollin (Singapore).

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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.

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Date/Time : 29 Jul 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Zhongkai Tao, Institut des Hautes Études Scientifiques

The fractal uncertainty principle, introduced by Dyatlov and Zahl, has become an important tool in the study of spectral gaps for systems with trapping. It quantifies how a function and its Fourier transform can both concentrate near fractal sets. I will talk about some recent progress in the fractal uncertainty principle and its applications to spectral problems. This talk is partly based on joint works with Aidan Backus, James Leng, Xiaoqi Huang, Christopher Sogge, Zhexing Zhang, Alex Cohen and Zhenhao Li.

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Date/Time : 29 Apr 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Juncheng Wei, The Chinese University of Hong Kong

In 2023, one year before his death, H. Brezis posted 28 open questions which he described as “challenging and difficult”. In this talk I will give complete answer to the first open question—Problem 1.1 on Brezis-Nirenberg problem on three dimensional unit ball, and the seventh open question—Problem 3.1 on harmonic map equation on disk.

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Date/Time : 25 Mar 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Jonathan Eskstein, Rutgers University

Parallel computing is a common tool in science and engineering. It is now common for large universities and government labs to own distributed HPC computing system with tens of thousands of processor cores, simulating phenomena such as protein folding, fluid flow, and structure deformation. However, other kinds of numerical computing have lagged behind in their use of large-scale parallel computing. In numerical optimization, the potential of parallel computing has not been fully exploited, except within specialized applications for neural network training. The most popular and robust optimization solver codes do not scale well beyond dozens of cores for some applications, and exhibit poor scaling after just a handful of cores in other cases. There are several reasons why, including the difficulty of parallelizing the central numerical operations in standard linear and nonlinear optimization algorithms, commitment to deterministic execution patterns, and programming difficulties. Languages and compilers for developing parallel algorithms have displayed little meaningful evolution in the last few decades even as hardware capabilities have soared; in fact, they have arguably devolved since the 1990’s.

However, the potential for using parallel computing in optimization remains. This talk will examine how numerical optimization solvers could more effectively take advantage of parallel computing, focusing on first-order methods for continuous optimization and search methods for discrete and nonconvex optimization. For truly challenging applications, it may be possible to combine such approaches. The talk will also discuss the potential obstacles and how they might be overcome. Time permitting, it will also overview some ongoing work on creating a portable parallel-capable version of the PDLP first-order linear programming solver.

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Date/Time : 11 Mar 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Sun Song, Zhejiang University

Einstein metrics serve as the counterpart in Riemannian geometry to Einstein spacetimes in general relativity. As one of the most important geometric structures, the study of Einstein metrics is deeply connected to various branches of mathematics, including complex algebraic geometry, low-dimensional topology, partial differential equations, and mathematical physics. In this talk we will discuss recent advances in understanding the construction and classification of Einstein metrics.

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Date/Time : 06 Mar 2026 14:30
Venue : IMS Executive Seminar Room (S17 Level 3)
Speaker : Max Welling, CuspAI & University of Amsterdam

Prof. Dr. Max Welling is a full professor and research chair in machine learning at the University of Amsterdam and a Merkin distinguished visiting professor at Caltech. He is co-founder and CTO of the startup CuspAI – a frontier AI company harnessing AI to unlock materials breakthroughs. He is also a member of the Royal Dutch Academy of Sciences, a fellow at the Canadian Institute for Advanced Research (CIFAR) and the European Lab for Learning and Intelligent Systems (ELLIS) where he served on the founding board. His previous appointments include Partner and VP at Microsoft Research, VP at Qualcomm Technologies, professor at UC Irvine.

Prof. Max Welling finished his PhD in theoretical high energy physics under supervision of Nobel laureate prof. Gerard ‘t Hooft. He then switched fields to focus on machine learning, first as a postdoc at Caltech under supervision of prof. Pietro Perona and then as postdoc under supervision of Nobel laureate prof. Geoffrey Hinton at UCL & U. Toronto.

Prof. Max Welling is a preeminent computer scientist and physicist with over 200,000 Google Scholar citations. His landmark contributions include inventing the Variational Autoencoder (VAE), a foundational architecture in generative AI, and Graph Convolutional Networks (GCNs), which revolutionized the processing of structured data such as molecules and social networks. Furthermore, he pioneered Stochastic Gradient Langevin Dynamics (SGLD) for Bayesian learning and has led the advancement of Equivariant Neural Networks, which integrate fundamental geometric symmetries into deep learning models.

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