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Week of April 1, 2026

April 2, 2026
Analysis [3] Incompressible Euler Blowup at the $C^{1,\frac{1}{3}}$ Threshold Steve Shkoller - University of California at Davis 4:00pm -
Zoom
Quantum Topology and Field Theory [4] Some algebra behind non-semisimple TQFTs Nathan Geer - Utah State University 4:30pm -
KT 801
April 3, 2026
Learning seminar on Matroids and Algebraic Cycles [5] Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801
Learning seminar on Groups, Geometry and Dynamics [6] Measures of maximal entropy. Ethan Cohen - 4:00pm -
KT 801 or KT217
April 6, 2026
Geometric Analysis and Application [7] Geometry of Mean Curvature Flow near Cylindrical Singularities Ao Sun - Lehigh University 3:45pm -
KT 906
Geometry, Symmetry and Physics [8] Elementary categorification of U_q(gl(1|1)) Alexei Oblomkov - U Mass Amherst 4:30pm -
KT 801
April 7, 2026
Geometric Analysis Learning Seminar [9] Geometric Analysis Learning Seminar 10:30am -
KT 801
April 9, 2026
Analysis [3] Completeness of reparametrization-invariant Sobolev metrics on the space of surfaces Martin Bauer - Florida State University 4:00pm -
Zoom
Quantum Topology and Field Theory [4] Summing over topologies in 3d gravity Scott Collier - Syracuse University 4:30pm -
KT 801
April 10, 2026
Learning seminar on Matroids and Algebraic Cycles [5] Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801
Learning seminar on Groups, Geometry and Dynamics [6] Learning seminar on Groups Geometry and Dynamics 4:00pm -
KT 801
April 13, 2026
Geometric Analysis and Application [7] Uniqueness of mean curvature flow evolution Tang-Kai Lee - Columbia University 3:45pm -
KT 906
Quantum Topology and Field Theory [4] Twistorial constructions of higher genus integrability Seraphim Jarov - Perimeter Institute 4:30pm -
KT 801
April 14, 2026
Geometric Analysis Learning Seminar [9] Geometric Analysis Learning Seminar 10:30am -
KT 801
Geometry & Topology [10] From Riemannian to Lorentzian: Embeddings of Signature-Changing Manifolds Nathalie Rieger - Yale University 4:00pm -
KT 203
April 15, 2026
Analysis [3] Global internal mode dynamics for the 1D quartic Klein-Gordon equation Gong Chen - Georgia Institute of Technology 4:00pm -
KT 205
April 16, 2026
Analysis [3] Concentration and fluctuations of sine-Gordon measure around topological multi-soliton manifold Philippe Sosoe - Cornell 4:00pm -
Zoom
Geometry, Symmetry and Physics [8] Malle's conjecture over function fields Aaron Landesman - Harvard 4:30pm -
KT 801
April 17, 2026
Quantum Topology and Field Theory [4] Cluster Configuration Spaces of Momentum Twistors Dani Kaufman - The Max Planck Institute for Mathematics in the Sciences 11:00am -
KT 801
Learning seminar on Matroids and Algebraic Cycles [5] Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801
Learning seminar on Groups, Geometry and Dynamics [6] Learning seminar on Groups Geometry and Dynamics 4:00pm -
KT 801
April 20, 2026
Geometry, Symmetry and Physics [8] Thesis defense: "On certain Lagrangian subvarieties in minimal resolutions of Kleinian singularities" Mengwei Hu - Yale University 4:30pm -
KT 801
April 21, 2026
Geometric Analysis Learning Seminar [9] Geometric Analysis Learning Seminar 10:30am -
KT 801
Geometry & Topology [10] On a conjecture of Ayala–Francis–Rozenblyum Ödül Tetik - University of Vienna 4:30pm -
KT 207
Geometry, Symmetry and Physics [8] Positivity of Canonical Bases Xuhua He - University of Hong Kong 4:30pm -
KT 801
April 23, 2026
Analysis [3] On the exact failure of the hot spots conjecture Mitchell Taylor - ETH Zürich 4:00pm -
KT 201
Quantum Topology and Field Theory [4] Triangulations and volume conjectures Fathi Ben-Aribi - Sorbonne-Université 4:30pm -
KT 801
April 24, 2026
Learning seminar on Matroids and Algebraic Cycles [5] Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801
Learning seminar on Groups, Geometry and Dynamics [6] Learning seminar on Groups Geometry and Dynamics 4:00pm -
KT 801
April 27, 2026
Geometry, Symmetry and Physics [8] Operator Representations, Twisted Traces and the Quantum Hikita Conjecture Keke Zhang - Perimeter Institute 4:30pm -
KT 801
April 28, 2026
Geometry, Symmetry and Physics [8] Thesis defense: Fourier coefficients of automorphic forms Joakim Faergeman - Yale 4:30pm -
KT 801

Abstracts

Week of April 1, 2026

April 2, 2026
Analysis [3] Incompressible Euler Blowup at the $C^{1,\frac{1}{3}}$ Threshold 4:00pm -
Zoom

We prove finite-time Type–I blowup for the three-dimensional incompressible Euler equations in the
axisymmetric no-swirl class, with initial velocity in $C^{1,\alpha}(\R^3)\cap L^2(\R^3)$ and odd
symmetry in $z$, for \emph{every} $\alpha\in(0,\tfrac13)$. Since axisymmetric no-swirl solutions
with $C^{1,\alpha}$ velocity are globally regular for $\alpha >\tfrac13$,  this result is sharp up to the
endpoint: it covers the entire open interval $(0,  \tfrac{1}{3})$,  reaching the structural regularity threshold
from below.

The singularity forms at the stagnation point on the symmetry axis, with vorticity and strain
blowing up at the Type–I rate $\|\bs{\omega}(\cdot,t)\|_{L^\infty}\sim(T^*-t)^{-1}$,
$-\partial_z u_z(0,0,t)\sim(T^*-t)^{-1}$, and the meridional Jacobian collapsing as
$J(t)\sim\big(\Gamma(T^*-t)\big)^{1/(1-3\alpha)}$.

The proof introduces a Lagrangian clock-and-driver framework that replaces the Eulerian self-similar
ansatz used in prior work. The collapse dynamics are governed by a Riccati-type ODE for the axial
strain, and the decisive step is a non-perturbative bound on the strain–pressure competition,
established via a spectral decomposition of the angular pressure source, showing that the quadratic
strain term dominates the resistive pressure Hessian uniformly for all $\alpha\in(0,\tfrac13)$.

The blowup mechanism is structurally stable: it persists for an open set of admissible angular
profiles in a weighted topology.
Quantum Topology and Field Theory [4] Some algebra behind non-semisimple TQFTs 4:30pm -
KT 801

In this talk I will give an introductory lecture on constructing Topological Quantum Field Theories (TQFTs) from non-semisimple categories. The main goal of the talk is to give a hint of what is needed to extend the Turaev-Viro and Crane-Yetter TQFTs from the useful setting of semisimple categories to the non-semisimple world.  I will do this from an algebraic and categorical point of view.  In particular, I will discuss what kind of structures are needed in non-semisimple categories to give rise to (2+1)-TQFTs.  Then I will remark that any spherical tensor category (in the sense of Etingof, Douglas et al.) has such structures.  This work is joint with Francesco Costantino, Benjamin Haïoun, Bertrand Patureau-Mirand and Alexis Virelizier and based on arXiv:2302.04509 and arXiv:2306.03225.
April 3, 2026
Learning seminar on Matroids and Algebraic Cycles [5] Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801

TBA
Learning seminar on Groups, Geometry and Dynamics [6] Measures of maximal entropy. 4:00pm -
KT 801 or KT217
April 6, 2026
Geometric Analysis and Application [7] Geometry of Mean Curvature Flow near Cylindrical Singularities 3:45pm -
KT 906

The cylindrical singularities are prevalent but complicated in geometric flows. We discuss one of the simplest extrinsic flows, the mean curvature flow, and illustrate how the local dynamics of the singularities influence the singular set itself, and the geometry and topology of the flow. This talk is based on a series of joint work with Zhihan Wang (Cornell) and Jinxin Xue (Tsinghua).
Geometry, Symmetry and Physics [8] Elementary categorification of U_q(gl(1|1)) 4:30pm -
KT 801

In joint work with Lev Rozansky we construct a coherent sheaf realization of the tensor powers of $U_q(gl(1|1))$ vector representation $\mathbb{C}^{1|1}$. The construction reveals the non-semisimple nature of the representation of $U_q(gl(1|1))$. I plan to explain how this
construction extends to а wider class of the representations. The origin of the construction is a boson/fremion correspondence in physics context and Legandre transformation in the mathematical context.
April 7, 2026
Geometric Analysis Learning Seminar [9] Geometric Analysis Learning Seminar 10:30am -
KT 801

TBA
April 9, 2026
Analysis [3] Completeness of reparametrization-invariant Sobolev metrics on the space of surfaces 4:00pm -
Zoom
The space of immersions of a closed manifold M into Euclidean space is among the most important infinite dimensional manifolds. The most natural Riemannian metrics on this space are reparametrization-invariant Sobolev metrics; these form a hierarchy of metrics, based on their order—the number of derivatives they “see”. They arise as natural extensions of right-invariant metrics on diffeomorphism groups, central to Arnold’s geometric formulation of hydrodynamical equations. Beyond their theoretical significance, they play a crucial role in mathematical shape analysis and geometric data science, where they enable meaningful and robust comparisons between shapes modeled as curves or surfaces. 
 
In 2013, David Mumford conjectured that for orders larger than dim(M)/2 + 1, these geometries are complete. Note, that by the seminal work of Ebin and Marsden a similar statement is known to be true for diffeomorphism groups. In the context of immersions this conjecture was shown to be true in the case of immersed curves in the work of Bruveris, Michor and Mumford. In this talk I will present the first construction of complete metrics on immersions of two-dimensional surfaces, discuss the context and techniques, as well as possible extensions to higher dimensions. Based on joint work with Cy Maor and Benedikt Wirth.
 
Quantum Topology and Field Theory [4] Summing over topologies in 3d gravity 4:30pm -
KT 801

I will describe recent progress towards understanding the gravitational path integral in AdS_3 quantum gravity and its boundary interpretation. A central question is: which spacetime topologies should be included in the path integral, and why? To address this question, we formulate a “statistical bootstrap” that constrains the universal statistics of CFT data in the boundary theory, imposing crossing symmetry and “typicality” (a generalization of the eigenstate thermalization hypothesis). These constraints are geometrized by iterative surgery moves on bulk manifolds that we refer to as the “gravitational machine,” leading to an infinite set of non-handlebody topologies that we argue must be included in the path integral. The machine generates only on-shell (hyperbolic) 3-manifolds, whose partition functions can be computed exactly using Virasoro TQFT. But not all hyperbolic manifolds are produced by this procedure. This reveals a large landscape of consistent sums over topologies. Based on joint work with Alexandre Belin, Lorenz Eberhardt, Diego Liska, and Boris Post.
April 10, 2026
Learning seminar on Matroids and Algebraic Cycles [5] Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801

TBA
Learning seminar on Groups, Geometry and Dynamics [6] Learning seminar on Groups Geometry and Dynamics 4:00pm -
KT 801

TBA
April 13, 2026
Geometric Analysis and Application [7] Uniqueness of mean curvature flow evolution 3:45pm -
KT 906

The smooth mean curvature flow often develops singularities, making weak solutions essential for extending the flow beyond singular times. Among various weak formulations, the level set flow method is notable for ensuring long-time existence and uniqueness. However, this comes at the cost of potential fattening, which reflects genuine non-uniqueness of the evolution after singular times. With Alec Payne, we establish an intersection principle comparing two intersecting flows and prove that level set flows satisfy this principle in the absence of non-uniqueness.
Quantum Topology and Field Theory [4] Twistorial constructions of higher genus integrability 4:30pm -
KT 801

I will present a new method to engineer integrable models in 4d with higher genus spectral parameters. The method has a twistorial origin - by working on a branched covering of twistor space, I show how one can derive deformations of holomorphic BF theory on twistor space which descend to elliptic and hyperelliptic models on R^4 via the Penrose transform. I show how one can bootstrap the Penrose transformed actions using symmetry and integrability to find deformations of self-dual Yang-Mills theory. I will also discuss some novel deformations of a BF type description of Hitchin’s equations. This is based on my recent paper: 2509.12486
April 14, 2026
Geometric Analysis Learning Seminar [9] Geometric Analysis Learning Seminar 10:30am -
KT 801

TBA
Geometry & Topology [10] From Riemannian to Lorentzian: Embeddings of Signature-Changing Manifolds 4:00pm -
KT 203

We examine a class of semi-Riemannian manifolds that undergo smooth metric signature change—from Riemannian to Lorentzian—across a hy- persurface with a transverse radical. This class includes physically mo- tivated cosmological models such as the Hartle-Hawking “no-boundary” proposal, in which the universe transitions smoothly from a Euclidean to a Lorentzian phase. We show that these manifolds admit isometric embeddings into higher-dimensional pseudo-Euclidean spaces and, in par- ticular, prove the existence of global isometric embeddings of the canonical model into both Minkowski and Misner spaces. This framework provides a mathematical setting for studying smooth signature change and its role in higher-dimensional and cosmological models.
April 15, 2026
Analysis [3] Global internal mode dynamics for the 1D quartic Klein-Gordon equation 4:00pm -
KT 205
We study the quartic Klein–Gordon equations with a potential in one space dimension as model problems and establish a global description of internal mode dynamics and radiation damping. It is well-known that internal modes not only decay slowly, but their amplitudes can also lose smallness at large times; combined with the slow dispersive decay in $1$ dimension, this makes the global analysis particularly delicate. Our approach is based on distorted Fourier transforms, normal form transformations, together with a collection of refined dispersive decay and smoothing estimates, which we exploit even at the level of the internal mode equation itself. This a joint work with Gael  Diebou, Adilbek Kairzhan and Fabio Pusateri. 
April 16, 2026
Analysis [3] Concentration and fluctuations of sine-Gordon measure around topological multi-soliton manifold 4:00pm -
Zoom
We study Gibbs measures formally defined by a Sine-Gordon Hamiltonian on long intervals on R, with a restriction on the winding number as a prototype of “topological solitions” in Euclidean field theories. We study concentration and fluctuations of the path around near minimizers of the action. 
 
Joint work with Kihoon Seong and Hao Shen.
Geometry, Symmetry and Physics [8] Malle's conjecture over function fields 4:30pm -
KT 801

For G a finite group, Malle’s conjecture predicts the asymptotic growth of the number of G extensions of a fixed global field. In joint work with Ishan Levy, we compute the asymptotic growth of the number of Galois G extensions of F_q(t), for q sufficiently large and relatively prime to |G|.  In the first part of the talk we will introduce Malle’s conjecture and explain how to reduce the above result to a homological stability result for spaces of G bundles. In the second part of the talk we will explain some of the key ideas in the proof of this homological stability result, which uses tools from higher algebra.
April 17, 2026
Quantum Topology and Field Theory [4] Cluster Configuration Spaces of Momentum Twistors 11:00am -
KT 801

The formalism of momentum twistors realises the kinematic space of 4-d planar N=4 SYM amplitudes as a configuration space of lines in P^3. All massless kinematics corresponds to consecutive lines intersecting which in turn is interpreted as a configuration of points in P^3, while massive kinematics corresponds to generic configurations of lines. I’ll give an overview of some current work in progress which aims to understand and relate cluster structures on each of these configuration spaces with an eye towards computing amplitudes using the symbol bootstrap. A key idea is to use “partial abelianiziation” of framed PGL_4 local systems on a surface to produce GL_2 local systems on a two fold spectral cover of the surface
Learning seminar on Matroids and Algebraic Cycles [5] Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801

TBA
Learning seminar on Groups, Geometry and Dynamics [6] Learning seminar on Groups Geometry and Dynamics 4:00pm -
KT 801

TBA
April 20, 2026
Geometry, Symmetry and Physics [8] Thesis defense: "On certain Lagrangian subvarieties in minimal resolutions of Kleinian singularities" 4:30pm -
KT 801

Abstract: Kleinian singularities are quotients of C^2 by finite subgroups of SL_2(C). They are in bijection with the ADE Dynkin diagrams via the McKay correspondence. In this talk, I will introduce certain singular Lagrangian subvarieties in the minimal resolutions of Kleinian singularities, motivated by the geometric classification of unipotent Harish-Chandra (g,K)-modules. The irreducible components of these singular Lagrangian subvarieties are P^1’s and A^1’s. I will describe how they intersect with each other through the realization of Kleinian singularities as Nakajima quiver varieties. I will also discuss their connections with nilpotent K-orbits and symmetric pairs in semisimple Lie algebras.

The defense will be preceeded by special tea at 3.30 in the lounge.
April 21, 2026
Geometric Analysis Learning Seminar [9] Geometric Analysis Learning Seminar 10:30am -
KT 801

TBA
Geometry & Topology [10] On a conjecture of Ayala–Francis–Rozenblyum 4:30pm -
KT 207

I will present some finite stratified homotopy types constructed from smooth data which are not the homotopy types of conically smooth manifolds, disproving a 2015 conjecture of Ayala, Francis and Rozenblyum. The main tool is a new combinatorial and fully faithful exit path infinity-category construction. Time permitting, I will discuss a future direction for such conjectures.
Geometry, Symmetry and Physics [8] Positivity of Canonical Bases 4:30pm -
KT 801

Lusztig’s theory of canonical bases reveals a remarkably rigid and positive algebraic structure on quantum groups and their modules. In symmetric types, it is known that the structure constants for multiplication in the negative part U −, as well as for the action of Chevalley generators Ei and Fi on a single simple module, all belong to N[v, v−1 ].

Lusztig conjectured that this strong positivity holds for the multiplication within the modified quantum group and the action on the tensor product of modules. In this talk, I will present recent joint work with Jiepeng Fang towards this conjecture.

 A key innovation in our approach is the ”thickening philosophy”, an algebraic technique inspired by geometric ideas from total positivity, building on my earlier work with Huanchen Bao. This method embeds a suitable approximation of the tensor product into the negative part U˜ − of a larger quantum group, constructed via a framed quiver. This allows us to inherit the desired positivity directly from the well-established positivity of the canonical basis of U˜ −. This approach demonstrates how the large Kac-Moody groups can provide a powerful framework for elucidating the structure and representations of quantum groups even for the finite and affine types.
April 23, 2026
Analysis [3] On the exact failure of the hot spots conjecture 4:00pm -
KT 201

The hot spots conjecture asserts that as time goes to infinity, the hottest and coldest points in an insulated domain will migrate towards the boundary of the domain. In this talk, I will describe joint work with Jaume de Dios Pont and Alex Hsu where we find the exact failure of the hot spots conjecture in every dimension.
Quantum Topology and Field Theory [4] Triangulations and volume conjectures 4:30pm -
KT 801

A volume conjecture relates a certain asymptotical growth of a given quantum topological invariant of a hyperbolic 3-manifold to the hyperbolic volume of this manifold.

In this talk I will mention several of these volume conjectures, their common points and differences, notably those associated to the Baseilhac-Benedetti invariants and to the Andersen-Kashaev TQFT.

A general strategy to prove a volume conjecture is to use the combinatorial properties of a given triangulation of the manifold to simplify the expression of the quantum invariant, and hopefully to successfully apply the saddle point method in the desired asymptotics.

I will use the figure-eight knot complement as a recurring example, as it is the simplest member of two infinite families, the hyperbolic twist knots and the once-punctured torus bundles over the circle.

No prerequisite in quantum topology or hyperbolic geometry will be needed.

(This talk will cover joint works with François Guéritaud, Stéphane Baseilhac and Ka Ho Wong)
April 24, 2026
Learning seminar on Matroids and Algebraic Cycles [5] Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801

TBA
Learning seminar on Groups, Geometry and Dynamics [6] Learning seminar on Groups Geometry and Dynamics 4:00pm -
KT 801

TBA
April 27, 2026
Geometry, Symmetry and Physics [8] Operator Representations, Twisted Traces and the Quantum Hikita Conjecture 4:30pm -
KT 801

Let $X$ and $X^{!}$ be a pair of dual conical symplectic singularities, and let $\tilde{X}^{!} \rightarrow X^{!}$be a symplectic resolution. The quantum Hikita conjecture states that the D-module of graded traces for $X$, is isomorphic to the specialized quantum D-module of $\tilde{X}^{!}$after localization. This talk introduces an operator-theoretic framework to construct these traces and apply them to the conjecture.

We discuss representation of quantized Homological and K theoretic Coulomb branches as operators acting on a two-parameter function space. This concrete representation provides a direct path to constructing integral form twisted traces for conical theories. 

Lastly, I will sketch a proof for a weaker version of the quantum Hikita conjecture by identifying these twisted traces with the vertex functions of quasimaps to the corresponding Higgs branch. This leads to the categorification of Jacobi-Trudi identity at principal specialization.
April 28, 2026
Geometry, Symmetry and Physics [8] Thesis defense: Fourier coefficients of automorphic forms 4:30pm -
KT 801

Abstract: we give a quick introduction to Fourier coefficients of modular forms and their importance in the Langlands program. We then turn to Fourier coefficients of automorphic forms over function fields and explain a micro-local interpretation of Fourier coefficients in this setting. The latter is joint work with Sam Raskin.

Preceded by special tea at 3.50pm in the lounge.
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Links
[1] https://calendar.math.yale.edu/list/calendar/grid/week/2026-W13 [2] https://calendar.math.yale.edu/list/calendar/grid/week/2026-W15 [3] https://calendar.math.yale.edu/seminars/analysis [4] https://calendar.math.yale.edu/seminars/quantum-topology-and-field-theory [5] https://calendar.math.yale.edu/seminars/learning-seminar-matroids-and-algebraic-cycles [6] https://calendar.math.yale.edu/seminars/learning-seminar-groups-geometry-and-dynamics [7] https://calendar.math.yale.edu/seminars/geometric-analysis-and-application [8] https://calendar.math.yale.edu/seminars/geometry-symmetry-and-physics [9] https://calendar.math.yale.edu/seminars/geometric-analysis-learning-seminar [10] https://calendar.math.yale.edu/seminars/geometry-topology [11] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2026-W13 [12] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2026-W15 [13] https://yale.zoom.us/j/95804422721