Seminars and Colloquia by Series

Distinguishing Exotic R^4's With Heegaard Floer Homology

Series
Geometry Topology Seminar
Time
Monday, February 23, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Sean Eli – Georgia Tech

This is joint work with Jen Hom and Tye Lidman. Attaching a Casson handle to a slice disk complement gives a smooth manifold homeomorphic to R^4. In the 90's De Michelis and Freedman asked how these choices affect the smooth type of the resulting manifold. This problem has seen some progress since then but is still not well understood. We show that if two slice knots have sufficiently different knot Floer homology, then the resulting exotic R^4's made with the simplest Casson handle are distinct. This gives a countably infinite family of exotic R^4's made with different slice disk complements. We then produce exotic R^4's with various phenomena, and re-prove a theorem of Bizaca-Etnyre on smoothings of product manifolds Y x R. Our main tool is Gadgil's end Floer homology, which we show how to compute effectively by analyzing a certain cobordism map. Time permitting, I'll discuss an upcoming result on exotic planes in R^4 and branched covers, and plans to study more noncompact exotic phenomena.

Formal GAGA for Brauer classes

Series
Algebra Seminar
Time
Monday, February 23, 2026 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Siddharth Mathur – University of Georgia

Please Note: There will be a pre-seminar at 10:55-11:25 in Skiles 005.

The relationship between analytic and algebraic geometry (GAGA) is a rich area of study. For example, Grothendieck's existence theorem states that if $X$ is proper over a complete local Noetherian ring $A$, then a compatible system of coherent sheaves on the thickenings $X_n$ of the special fiber is algebraizable. Such GAGA-type results are now standard tools for studying varieties and their families. In this talk, we answer a question Grothendieck posed in the 1960s: can a Brauer class on $X$ be determined from a compatible system of classes on the $X_n$'s? This is joint work with Andrew Kresch.

Introduction to Teichmuller theory, classical and higher rank III

Series
Geometry Topology Working Seminar
Time
Friday, February 20, 2026 - 14:00 for 2 hours
Location
Skiles 006
Speaker
Mike Wolf – Georgia Tech

We give an overview of Teichmuller theory, the deformation theory of Riemann surfaces. The richness of the subject comes from all the perspectives one can take on Riemann surfaces: complex analytic for sure, but also Riemannian, topological, dynamical and algebraic.  In the past 40 years or so, interest has erupted in an extension of Teichmuller theory, here thought of as a component of the character variety of surface group representations into PSL(2,\R), to the study of the character variety of surface group representations into higher rank Lie groups (e.g. SL(n, \R)). We give a even breezy  discussion of that.

 

Incommensurate Twisted Bilayer Graphene: emerging quasi-periodicity and stability

Series
Math Physics Seminar
Time
Friday, February 20, 2026 - 11:00 for 1 hour (actually 50 minutes)
Location
Skyles 006
Speaker
Vieri Mastropietro – Universita' di Roma “La Sapienza”, Department of Physics, Rome, Italy –
We consider a lattice model of twisted bilayer graphene (TBG) for incommensurate twist angles, focusing on the role of large-momentum-transfer Umklapp terms. These terms, which nearly connect the Fermi points of different layers, are typically neglected in effective continuum descriptions but could, in principle, destroy the Dirac cones; they are indeed closely analogous to those appearing in fermions within quasi-periodic potentials, where they play a crucial role. We prove that, for small but finite interlayer coupling, the semimetallic phase is stable provided the angles belong to a fractal set of large measure (which decreases with the hopping strength) characterized by a number theoretic Diophantine condition. In particular, this set excludes the (zero measure) commensurate angles. Our method combines a Renormalization Group (RG) analysis of the imaginary-time, zero temperature Green’s functions, with number theoretic properties, and is similar to the technique used in the Lindstedt series approach to Kolmogorov-Arnold-Moser (KAM) theory. The convergence of the resulting series allows us to rule out non-perturbative effects. The result provides a partial justification of the effective continuum description of TBG in which such large-momentum interlayer hopping processes are neglected.
Work in collaboration with Ian Jauslin
 
Available on zoom at: 
https://gatech.zoom.us/j/92212527205?jst=4
 

The least prime with a given cycle type

Series
Number Theory
Time
Wednesday, February 18, 2026 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Robert Lemke-Oliver – University of Wisconsin –

The Chebotarev density theorem is a powerful tool in number theory, in part because it guarantees the existence of primes whose Frobenius lies in a given conjugacy class in a fixed Galois extension of number fields.  However, for some applications, it is necessary to know not just that such primes exist, but to additionally know something about their size, say in terms of the degree and discriminant of the extension.  In this talk, I'll discuss recent work with Peter Cho and Asif Zaman on a closely related problem, namely determining the least prime with a given cycle type.  We develop a new, comparatively elementary approach for thinking about this problem that nevertheless frequently yields the strongest known results.  We obtain particularly strong results in the case that the Galois group is the symmetric group $S_n$ for some $n$, where determining the cycle type of a prime is equivalent to Chebotarev.

Generalized Colouring of Planar Graphs

Series
Graph Theory Seminar
Time
Tuesday, February 17, 2026 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Evelyne Smith-Roberge – Illinois State University

In the mid 1990s, Thomassen proved that planar graphs are 5-list-colourable, and that planar graphs of girth at least five are 3-list-colourable. Moreover, it can be shown via a simple degeneracy argument that planar graphs of girth at least four are 4-list-colourable.  In 2021, Postle and I unified these results, showing that if $G$ is a planar graph and $L$, a list assignment for $G$ where all vertices have size at least three; vertices in 4-cycles have list size at least four; and vertices in triangles have list size at least five, then $G$ is $L$-colourable. In this talk, I will discuss a strengthening of this latter result: that it also holds for correspondence colouring, a generalization of list colouring. In fact, it holds even in the still stronger setting of weak degeneracy. I will also speak briefly on some other weak degeneracy results in the area.

No prior knowledge of correspondence colouring nor list colouring will be assumed.  (Ft. joint work with Ewan Davies, and with Anton Bernshteyn and Eugene Lee.)

A combinatorial model for higher tropical Grassmannians

Series
Representation Theory, Moduli, and Physics Seminar
Time
Tuesday, February 17, 2026 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Nick Early – Institute for Advanced Study

The tropical Grassmannian Trop G(k,n), introduced by Speyer and Sturmfels, parametrizes tropical linear spaces in tropical projective space. For k=2, it can be identified with the space of phylogenetic trees. Beyond applications to mathematical biology, it has seen striking new connections in physics to generalized scattering amplitudes via the CEGM framework.

Despite this, constructing a combinatorial model for the positive tropical Grassmannian at higher k has remained an open problem. I will describe such a model built from the planar basis, a distinguished basis of the space of tropical Plücker vectors whose elements are rays of the positive tropical Grassmannian, together with a duality between tropical u-variables and noncrossing tableaux, which provides an explicit inverse to the Speyer–Williams parameterization. For k=3, the model connects to SL(3) representation theory via a cross-ratio formula that computes tropical invariants directly from non-elliptic webs, and to CAT(0) geometry via diskoids in affine buildings.

Based on joint work with Thomas Lam.

4-ended Tangles, Heegaard Floer Homology, and Norm Detection

Series
Geometry Topology Seminar
Time
Monday, February 16, 2026 - 16:30 for 1 hour (actually 50 minutes)
Location
Boyd 322, University of Georgia
Speaker
Fraser Binns – Princeton

Link Floer homology is a powerful invariant of links due to Ozsváth and Szabó. One of its most striking properties is that it detects each link's Thurston norm, a result also due to Ozsváth and Szabó. In this talk I will discuss generalizations of this result to the context of 4-ended tangles, as well as some tangle detection results. This is joint work in progress with Subhankar Dey and Claudius Zibrowius.

Real Heegaard Floer homology and localization

Series
Geometry Topology Seminar
Time
Monday, February 16, 2026 - 15:00 for 1 hour (actually 50 minutes)
Location
UGA Boyd 322
Speaker
Kristen Hendricks – Rutgers

In the past few years there have been a host of remarkable topological results arising from considering "real" versions of various gauge and Floer-theoretic invariants of three- and four-dimensional manifolds equipped with involutions. Recently Guth and Manolescu defined a real version of Lagrangian Floer theory, and applied it to Ozsváth and Szabó's three-manifold invariant Heegaard Floer homology, producing an invariant called real Heegaard Floer homology associated to a 3-manifold together with an orientation-preserving involution whose fixed set is codimension two (for example a branched double cover). We review the construction of real Heegaard Floer theory and use tools from equivariant Lagrangian Floer theory, originally developed by Seidel-Smith and Large in a somewhat different context, to produce a spectral sequence from the ordinary to real Heegaard Floer homologies in their simplest "hat" version, in particular proving the existence of a rank inequality between the theories. Our results apply more generally to the real Lagrangian Floer homology of exact symplectic manifolds with antisymplectic involutions. Along the way we give a little history and context for this kind of result in Heegaard Floer theory. This is a series of two talks; the first "prep" talk will discuss some background and context that might be helpful to (for example) graduate students in attendance.

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