Fall 2026
November 5: Eliott Gathercole (Koç Univesity, Turkey)
Title: Periodic structures on symplectic cohomology of orbifold divisor complements
Abstract: Symplectic cohomology, SH(W), is an algebra obtained from certain exact symplectic manifolds W. In particular, smooth complex affine varieties can be equipped with exact symplectic structures and SH is an invariant of the variety. SH(W) contains much information about the symplectic geometry of W, and is highly relevant to mirror symmetry. We consider cases where the affine variety W has an orbifold compactification, meaning it can be realised as the complement of a complex orbifold inside a projective variety.
In this talk, I will first give an introduction to the definition and properties of SH. I will then outline a result (forthcoming joint work with Bogdan Simeonov) which states that, when W admits an orbifold compactification, and satisfies further mild technical assumptions, we obtain a distinguished element M of SH(W), such that multiplication by M induces a periodic structure. I will discuss how this result relates to existing computations of SH* using various kinds of compactifications, give a sketch of the proof, an describe an application, to computing SH(W) where W is the complement of a star-shaped configuration of rational curves in a K3 surface.
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November 3: Aashraya Jha (Bilkent Univ, Turkey)
Title: From Triangles to Tori: p-adic methods for the classification of geometric objects
Abstract: Can a right triangle and an isosceles triangle have the same area and perimeter? Questions like this lead naturally to rational points on curves, where geometry helps us understand rational solutions to polynomial equations. We will explore how the geometry of a curve shapes its rational points, before turning to modular curves: curves that encode elliptic curves and the Galois symmetries of their torsion points. I will discuss recent joint work determining the rational points on a modular curve of genus 12, completing the classification of 3-adic Galois images for non-CM elliptic curves over the rationals. Time permitting, we will look at some of the p-adic methods that make such calculations possible, including Chabauty–Coleman and quadratic Chabauty. The talk is intended for a general mathematical audience.
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October 22: Taoufik Hmidi (New York University Abu Dhabi, UAE)
Title: Non-Rigid Time-Periodic Solutions to the Euler Equations in Bounded Domains
Abstract: In this talk, I will discuss several aspects of vortex dynamics for the two-dimensional Euler equations, with particular emphasis on the construction of time-periodic solutions. In the first part, I will review some results on the desingularization of point-vortex configurations leading to rigidly rotating or translating solutions. In the second part, I will focus on vortex motion in bounded planar domains. It is well known that, in a convex domain, the motion of a single point vortex is periodic. We will show that almost all of these periodic trajectories can be desingularized into time-periodic solutions consisting of concentrated vortex patches. The proof relies on a combination of KAM techniques, Nash-Moser scheme and tools from complex analysis.
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Spring 2026
May 14: Waqar Ali Shah (Bilkent University)
Title: Eisenstein Classes and Norm Relations
Abstract: Eisenstein symbols are cohomological avatars of classical Eisenstein series
and are among the most explicit classes appearing in the conjectures of
Beilinson and Bloch--Kato. In the setting of modular curves, they were
introduced by Beilinson, who related their regulators to special values of
L-functions. One of Kato's key insights was that these classes can also
be organized into Euler systems, leading to powerful arithmetic applications
for Selmer groups of modular forms.
In this talk, I will begin with a gentle introduction to Kato's Euler system, focusing
on the key ingredient known as norm compatibility: as the level of the
modular curve varies, traces of cohomology classes are governed by Hecke
operators that specialize to Euler factors of modular forms. I will then
discuss a conceptual reformulation of this norm-compatibility condition,
formulate some general results, and explain how these enter recent
Euler-system constructions on higher-dimensional Shimura varieties.
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April 23 (Thursday): Joan Mateo (Univesitat Autònoms de Barcelona)
Title: Explicit minimisers for anisotropic Riesz energies.
Abstract: We will characterize energy minimisers for a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisotropic. We will show that, if the Fourier transform of the repulsive potential is positive, the minimiser is supported on a fully-dimensional ellipsoid, and its density is given by a Barenblatt-type profile. We will explain which is the connection of this problem of minimisers with dislocations in material sciences.
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April 10 (Friday): Christiaan Van de Ven (Friedrich-Alexander‑Universität Erlangen‑Nürnberg)
Title: Algebraic quantum theory and applications to physics
Abstract: In this seminar, I will present results from my research on the rigorous analysis of classical and macroscopic limits of quantum systems. First, I will show how the algebraic framework of deformation quantization and continuous C*-bundles can be exploited to study these limits, illustrated with explicit examples.
Next, I will discuss how the infinite-volume (thermodynamic) limit naturally aligns with quantization theory, allowing a precise characterization of the uniqueness of KMS equilibrium states in both infinite classical and quantum spin systems. I will also briefly highlight the main techniques and their extension to unbounded models via the celebrated resolvent algebras.
Finally, I will discuss the connection to large deviation theory for semi-classical probability measures, providing a sophisticated framework to describe the quantum fluctuations of the system.
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May 5: Tianyu Yuan (Eastern Institute of Technology at Ningbo)
Title: Morse theory on symmetric products and quantized nonabelianization
Abstract: We introduce folded Morse flow trees, which provides a Morse theory on symmetric products with bulk deformation. First we show that a local computation recovers finite Hecke algebras. Then we show its relation to quantized nonabelianization: Gaiotto-Moore-Neitzke introduced the notion of spectral network in the study of supersymmetric gauge theory. It provides a way to define a nonabelianization map (UV-IR map) from gl(1) local systems on a spectral curve to gl(N) local systems on the base surface. Neitzke-Yan considered a quantization of this map between skein algebras. In this work, we consider a different quantization in the sense of braid skein algebras using both Floer and Morse approach. This is joint work with Ko Honda and Yin Tian.
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March 26: Daniyar Omarov (University of Alberta)
Title: Numerical Methods for Optimal Transport Problems
Abstract: In my talk, I present numerical methods for solving optimal transport (OT) problems in two settings. First, I study the classical continuous OT problem with the squared Euclidean cost and compare several numerical approaches, including two methods based on the fluid dynamics formulation and a direct discretization of the Monge–Ampère equation. I also introduce a class of problems called ''separable'', for which highly accurate numerical methods can be developed.
I then present a novel implementation of Newton’s method for semi-discrete OT problems with cost functions given by positive combinations of (p)-norms, (1 < p < \infty). By exploiting the geometry of Laguerre cells, the method provides an efficient and robust way to compute the associated network structure, with potential applications including cost interpolation and electoral districting.
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April 9 (Thursday): Billel Guelmame (NYUAD, UAE )
Title: On regularized nonlinear hyperbolic equations
Abstract: In this talk, we present non-diffusive and non-dispersive regularizations of the inviscid Burgers equation and the barotropic Euler equations. We study the existence of both local-in-time and global solutions. In addition, in the scalar case, we show that, taking the singular limit, the regularized model converges in strong topologies to the original equation.
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April 7: Bahar Acu (Bogazici University - Pitzer College)
Title: Open Books and Singular Fibrations in Higher-Dimensional Contact Topology
Abstract: A key approach to studying a topological manifold is to decompose it into simpler pieces via fibrations. An important example is an open book decomposition, which presents a manifold as pages glued together along a common binding. Open books offer a powerful framework for analyzing special odd-dimensional smooth manifolds, contact manifolds, that shifts the study of these geometric objects to a topological perspective. In this talk, I will describe how special singular symplectic fibrations give rise to open book decompositions and how this perspective can be used to systematically produce and study higher-dimensional contact manifolds.
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March 24: Mohamed Amine Lkabous (University of Southampton)
Title: From Distress to Recovery: Optimal Triggers for Expand/Contract Decisions
Abstract: We study when a firm has truly emerged from a prolonged spell of financial distress, formalized as the last time its performance stays below a health threshold for at least a chosen duration. We pose an optimal prediction problem: choose a stopping time that minimizes absolute distance to that endpoint. The solution is a barrier rule with two regimes: a constant trigger or a time-varying boundary. On the applied side, this yields an expand/contract/wait strategy: set reference levels for expansion and contraction, and act when the observed metric crosses the data-driven boundary.
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February 24: Mattia Manucci (Karlsruhe Institute of Technology)
Abstract: Model Order Reduction (MOR) provides an effective framework for simplifying large-scale mathematical models—particularly those arising from partial differential equations (PDEs) and high-dimensional dynamical systems—by reducing computational complexity while preserving essential system behaviour. In this talk, we focus on the efficient and certified numerical approximation of parametric Hermitian eigenproblems, with particular attention to computing the smallest eigenvalue and its associated eigenspace. Such parametric eigenvalue problems play a central role in diverse applications, including parametric PDEs and quantum spin systems (QSS), and are typically computationally demanding and inherently multi-query, requiring repeated evaluations across a parameter range.
Our approach is based on projection-based MOR, in which the original high-dimensional problem is projected onto a carefully constructed low-dimensional subspace. This subspace is built using weak-greedy algorithms applied over continuous or discrete parameter sets. A crucial ingredient in any greedy strategy is the availability of reliable and efficiently computable error estimates. We derive a novel a posteriori error estimator tailored to the approximation of the eigenspace associated with the smallest eigenvalues.
The key insight is that accurate approximation of the spectral gap—the separation between the smallest and second-smallest eigenvalues—combined with exact recovery of the eigenspace dimension in the projected problem, enables rigorous certification of the eigenspace approximation error.
We conclude with numerical experiments demonstrating the performance of the proposed methodology on QSS models, including the XXZ and BBQ chain models.
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February 19: Volker Mehrmann (Technical University of Berlin)
Title: Spectral Theory of Infinite Dimensional Dissipative Hamiltonian Systems
Abstract: The spectral theory for operator pencils and operator differential-algebraic equations is
studied. Special focus is laid on singular operator pencils and three different concepts of
singularity of operator pencils are introduced. The concepts are analyzed in detail and examples
are presented that illustrate the subtle differences. It is investigated how these concepts
are related to uniqueness of the underlying algebraic-differential operator equation, showing
that, in general, classical results known from the finite dimensional case of matrix pencils
and differential-algebraic equations do not prevail. The results are then studied in the setting
of structured operator pencils arising in dissipative differential-algebraic equations. Here,
unlike to the general infinite-dimensional case, the uniqueness of solutions to dissipative
differential-algebraic operator equations is closely related to the singularity of the pencil.
Joint work with Christian Mehl und Michal Wojtylak