Date/Time : 06 Apr 2026 10:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Siyuan Tang, Xiamen University

We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces. In particular, we obtain an effective closing lemma on $\mathcal{H}(2)$. More precisely, we show that unless a small discriminant Teichmüller curve near $x\in\mathcal{H}(2)$, the geodesic push-forward of horocycle orbit $a_{t}u_{[0,1]}x$ has the discretized fractal dimension near 1 in a direction transverse to the $SL_{2}(\mathbb{R})$-orbit. The proofs make use of spectral gaps, of the Margulis function technique, and of the classification of Teichmüller curves in $\mathcal{H}(2)$.

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Date/Time : 30 Mar 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ian Gleason, National University of Singapore

This is a sequel to the previous talk. In this talk I will describe the challenges tackled in order to construct the comparing functor. Depending on time constraints, I might also discuss the strategy to show that the constructed functor is an equivalence.

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Date/Time : 30 Mar 2026 10:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Luis Vega, University of the Basque Country (UPV/EHU), Spain

I’ll present some recent work about the connection of vortex filaments/tubes that move according to Navier Stokes Equation and the binormal curvature flow of curves in 3d. This is a joint work with Marco A. Fontelos and Mikel Ispizua.

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Date/Time : 30 Mar 2026 16:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Schwab Christoph, ETH Zurich, Switzerland

We report mathematical results on numerical methods for the fractional Laplacian. Emphasis will be on polygonal and polyhedral domains, weighted analytic regularity of solutions and exponential convergence results for hp-Galerkin Finite Element Approximation of solutions. Integral and spectral fractional Laplacians will be considered.

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Date/Time : 27 Mar 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Wu Xingyu, National University of Singapore

Let F be a local field and let G be a split exceptional group over F. The theta correspondence for the dual pair (SL2, G) relates irreducible representations of SL2(F) and G(F), and a basic problem is to determine which representations of G(F) occur in the lift and with what multiplicity. In this talk, based on Hanzer and Savin’s work, I will explain a multiplicity-one statement for an oscillator-type model attached to a fixed additive character, and how it leads to a classification of those irreducible representations of G(F) that appear as its quotients. As a consequence, one obtains a clean criterion: a representation of G(F) occurs precisely when it is the theta lift of a generic irreducible representation of SL2(F). I will sketch the main ideas behind this reduction and indicate how it guides the computation of the correspondence.

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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 : 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 : 25 Mar 2026 14:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Farhad Babaee, University of Bristol

I will discuss several basic concepts in tropical geometry and explain how certain results in tropical geometry can be understood within the framework of the continuity of slices of tropical currents. This talk is based on joint work with Tien Cuong Dinh.

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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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