Date/Time : 17 Mar 2026 15:00
Venue : IMS Executive Seminar Room (S17 Level 3)
Speaker : Mihai Anitescu, Argonne National Laboratory and University of Chicago

Since 2018, with several co-authors, we have pursued a research program to explain a phenomenon first observed in long-horizon optimal control problems. That is when the data of the problem is perturbed at a certain temporal index, the effect of the perturbation on the solution at a different temporal index decays exponentially fast with respect to the distance between the two. We have shown, that, under uniform second order and linear independence constraint qualifications this phenomenon holds and we extended this proof for spatially-indexed, and more generally, graph-indexed problems. In turn, this allows proving that Schwarz-type decompositions with overlap used as either preconditioners or as solution schemes improve convergence exponentially fast with the size of the overlap. We discuss the consequences of this observation for design of efficient parallel algorithms and decentralized optimization schemes and present a few of their applications.

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Date/Time : 16 Mar 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ian Gleason, National University of Singapore

We show a folklore conjecture stating that two categorical enhancements of the automorphic side of the local Langlands correspondence agree. The first enhancement appears in Fargues–Scholze’s formulation of the categorical local Langlands correspondence, and the second one appears in Zhu’s formulation. This is joint work with Hamann, Ivanov, Lourenco, Zou.

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Date/Time : 16 Mar 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Svetlana Makarova, Australian National University

When introducing the notion of moduli problems, perhaps the most trivial example one may consider is the “functor of points” of a variety X, whose “classifying space” (moduli space) is X itself. Its very close relative is the stack of ideal sheaves of length 1 subschemes: when X is normal and of dimension at least 2, this stack is the product of X with BG_m. Despite the apparent triviality, modifying this stack gives rise to interesting birational phenomena, about which I will speak. I will describe a certain enlargement U of the stack of ideal sheaves that yields, via taking the good moduli space, a birational contraction of X, and an open substack of U that yields a surgery diagram via non-GIT wall-crossing. If time permits, I will explain how the interpretation of the surgery as a fine moduli of sheaves helps prove instances Kawamata’s DK-hypothesis in this setting. This is joint work with Andres Fernandez Herrero (https://arxiv.org/abs/2508.13395).

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Date/Time : 13 Mar 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Leong Jin Ming, National University of Singapore

The Theta correspondence and Springer correspondence are important tools in representation theory, each having a different flavour. During the Relative Langlands conference in January, Zhiwei Yun gave a talk on his recent paper with Jiajun Ma, Congling Qiu, and Jialiang Zou in which they managed to reduce Theta correspondence to Springer correspondence. I will introduce the correspondences, give a brief summary of their findings, and then explain a conjectural manifestation of relative Langlands duality between Theta and Gan-Gross-Prasad via Springer theory.

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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 : 11 Mar 2026 16:15
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Viet-Anh Nguyen, Universite de Lille

Let T be a positive dd^c-closed current of bidimension (1,1) on a projective manifold X. We show that for every c > 0 the set of points of X where the Lelong number of T is larger or equal to c is an analytic subset of dimension at most 1 of X. Moreover, the following Siu decomposition holds

T=\sum_{i\in I} λ_i[V_i] + T_0,

where {V_i}_{i\in I} is a (possibly empty) finite or countable family of compact analytic curves
in X, λ_i\in R^+, and T_0 is a positive dd^c-closed current of bidimension (1,1) on X whose Lelong number vanishes outside a finite or countable set. As a consequence, the cohomology class of every positive dd^c-closed current of bidimension (1,1) on X, which does not give mass to any proper analytic set, belongs to the movable cone M. This is a joint-work with Tien-Cuong Dinh.

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Date/Time : 11 Mar 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Nguyen Thi Van Anh, Hanoi National University of Education

The Allen–Cahn equation is a reaction–diffusion equation of mathematical physics which describes the process of phase separation in multi-component alloy systems, including order-disorder transitions. The relation between the approximate Allen–Cahn equations and mean curvature flow has been an ongoing investigation for several decades. For well-prepared initial conditions, Evans, Soner, and Souganidis proved the convergence to the viscosity solutions, Ilmanen showed convergence results to a Brakke flow, and many others. For a general initial conditions, Alfaro, Hilhorst and Matano carried out an analysis showing that the solution develops a steep transition layer within a specific time scale of parameters. In this talk, I will consider the Allen-Cahn equation under the initial condition that is no longer well-prepared and even discontinuous, in particular it is simply as a ‘signed function’ of a given set. The solvability of problems, the convergence to the mean curvature flows in both classical and weak sense are discussed. This is a part of an ongoing research project with Giovanni Bellettini.

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Date/Time : 11 Mar 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Georg Weiss, University of Duisburg-Essen

While global solutions of the obstacle problem have recently been completely characterized (Eberle-Figalli-Weiss 2025), the class of global solutions to the Bernoulli problem is, by a result of M. Traizet (2013), much richer and closely related to minimal surfaces.

In this talk, we explain why a frequency formula of the type used in the obstacle problem is unlikely to be valid for the Bernoulli problem. We also present progress on a different approach—one that does not rely on complex analysis—which appears to be a promising alternative for studying global solutions of the Bernoulli problem.

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Date/Time : 11 Mar 2026 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Zhang Xiaoyan, National University of Singapore

Chaitin’s Omega is defined to be the halting probability of a randomly constructed program. Equivalently it can be defined by the sum of Kolmogorov weights of all binary strings. In this talk we investigate the Omega function f that maps a real x to the sum of Kolmogorov weights of all strings on the left of x. We establish properties of f and compare it with previously defined Omega-related functions. We present that (i) f is strictly increasing, continuous and differentiable precisely at density random reals; (ii) The range of f is a null, nowhere dense, perfect Pi01(0′) class with Hausdorff dimension 1; (iii) there are continuum many x such that f(x) is not random.

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