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 : 25 Mar 2026 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Josiah Jacobsen-Grocott, Nanyang Technological University

Hyperenumeration reducibility was first introduced by Sanchis. A set $A$ is hyperenumeration reducible to $B$, $A\le_{he} B$, if there is a c.e.\ set $W$ such that
$x\in A \iff \forall f\in \omega^{\omega}\exists v,n \in \omega [\langle f{\restriction} n,x,v\rangle\in W \land D_v\subseteq B]$. The relationship between hyperenumeration and hyperarithmetic reducibility shares many parallels with the relationship between enumeration and Turing reducibility, like the fact that the hyperarithmetic degrees properly embed into the hyperenumeration degrees. However, not all properties transfer from the enumeration degrees; for instance, Selman’s Theorem is known to be false in the hyperenumeration degrees.

In this talk we look the downwards density property of the enumeration degrees, and show that it does transfer to the hyperenumeration degrees. This involves transferring injury arguments from a finite context into constructions in $L_{\omega_1^{CK}}$, and finding tools to overcome some of the limitations of hyperenumeration operators.

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Date/Time : 20 Mar 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Lucas Mason-Brown, University of Texas at Austin

Let G be a reductive group defined over a local field F. The local Langlands conjecture suggests a correspondence between (certain) infinite-dimensional irreducible G(F)-representations and (certain) finite-dimensional representations of the absolute Galois group \Gamma_F of F. If E/F is a field extension, then there is an inclusion \Gamma_F \subset \Gamma_E, and hence a natural map (restriction) from \Gamma_E-representations to \Gamma_F-representations. Composing with the (conjectural) Langlands correspondences for G(E) and G(F), we obtain a (conjectural) map, called `base change’ from G(F)-representations to G(E)-representations. In this talk, I will consider the special case when E=C and F=R. For real and complex groups, the local Langlands conjecture is a theorem (at least on the level of K groups), so there is a well-defined base change map from G(R)-representations to G(C)-representations (at least on the level of K groups). An interesting problem is to describe this correspondence directly, i.e. without appealing to the Langlands classification. I will describe a *partial* solution to this problem, following work of Clozel. Time permitting, I will formulate some conjectures regarding preservation of unitarity. This is joint work in progress with Andrei Ionov and David Nadler.

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Date/Time : 18 Mar 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Zihui Zhao, Johns Hopkins University

Free boundary problems are problems of solving an elliptic or parabolic PDE, but on a domain that is determined by the solution, and they arise naturally in the study of water waves and ice melting, etc. In this talk, we will focus on the regularity of the free boundaries for the Bernoulli problem, firstly studied by Alt and Caffarelli. More precisely, we study the behavior of such solutions near some well-known singularity models. In particular, our result implies that such singularity is not the typical behavior. This is joint work with Engelstein and Restrepo.

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Date/Time : 18 Mar 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Lucas Mason-Brown, University of Texas at Austin

A basic unsolved problem in representation theory is to classify the set of irreducible unitary representations of a reductive Lie group G. In this talk, I will describe a geometric approach to this problem, which has emerged over the past several years, based on the theory of quantizations of symplectic singularities. I will formulate a precise conjectural classification of the irreducible unitary representations of an arbitrary group G and present some recent progress towards its proof.

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Date/Time : 18 Mar 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Fan Chang, Nankai University

In this talk, I will present a short and elementary proof of the Poincaré inequality for increasing subsets of the hypercube, recently proved by Fei and Ferreira Pinto Jr. This result implies an $O(n^2)$ upper bound on the mixing time of censored random walks, improving on the earlier $O(n^3)$ bound of Ding and Mossel. This is joint work with Guowei Sun and Lei Yu.

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Date/Time : 18 Mar 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Sam G. Krupa, École Normale Supérieure, Paris

For hyperbolic systems of conservation laws in 1-D, fundamental questions about uniqueness and blow up of weak solutions still remain even for the apparently “simple” systems of two conserved quantities such as isentropic Euler and the p-system. Similarly, in the multi-dimensional case, a longstanding open question has been the uniqueness of weak solutions with initial data corresponding to the compressible vortex sheet. We address all of these questions by using the lens of convex integration, a general method of constructing highly irregular and non-unique solutions to PDEs. Our proofs involve computer-assistance. This talk is based on joint work with László Székelyhidi, Jr.

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Date/Time : 18 Mar 2026 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Stefan Ludwig, University of Freiburg

What is the common theory of all finite fields equipped with an additive and/or multiplicative character? Hrushovski answered this question in the additive case working in (a mild version of) continuous logic. Motivated by natural number-theoretic examples we generalise his results to the case allowing for both (non-trivial) additive character and (sufficiently generic) multiplicative character. Apart from answering the above question we obtain a quantifier elimination result and a generalisation of the definability of the Chatzidakis-van den
Dries-Macintyre counting measure to this context. The proof relies on classical results on bounds of character sums following from the work of Weil.

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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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