Geometry Topology Dynamical Systems Seminar
AY 202122
Unless otherwise noted, the GTDS Seminar will be held on Mondays @ 3pm at FO 2.404.
For online seminars, zoom link will be shared in this page.
Date 
Speaker/Institution 
Title/Abstract 
Oct 11 at 11am GR 2.302 
MIT 
Noncollapsed degeneration and desingularization of Einstein 4manifolds 
Oct 11 
Rice U. 
A nonlinear spectrum on closed manifolds 
Oct 18 at 2pm online talk 
MIT 

Oct 25 at 2pm GR 4.204 
UT Dallas 
Asymptotically conical CalabiYau manifolds 
Nov 1 
UT Dallas 
Renormalized Area for 4dimensional Minimal Hypersurfaces of a PoincaréEinstein Space 
Nov 8 
OK State 

Nov 15 online talk 
OK State 

Nov 22 
Fall Break


Nov 29 online talk 
Texas A&M 
For questions about the seminar, please contact Baris Coskunuzer
Archive of talks from previous semesters
Noncollapsed degeneration and desingularization of
Einstein 4manifolds
Tristan Ozuch (MIT) October 11, 2021
We study the moduli space of unitvolume Einstein 4manifolds near its finitedistance boundary, that is, the noncollapsed singularity formation. We prove that any smooth Einstein 4manifold close to a singular one in a mere GromovHausdorff (GH) sense is the result of a gluingperturbation procedure that we develop and which handles the presence of multiple trees of singularities at arbitrary scales. This sheds some light on the structure of the moduli space and lets us show that spherical and hyperbolic orbifolds which are Einstein in a synthetic sense cannot be GHapproximated by smooth Einstein 4manifolds.
A nonlinear spectrum on closed manifolds
Christos Mantoulidis (Rice U.) October 11, 2021
The pwidths of a closed Riemannian manifold are a nonlinear analogue of the spectrum of its Laplace–Beltrami operator, which was defined by Gromov in the 1980s and corresponds to areas of a certain minmax sequence of hypersurfaces. By a recent theorem of Liokumovich–Marques–Neves, the pwidths obey a Weyl law, just like the eigenvalues do. However, even though eigenvalues are explicitly computable for many manifolds, there had previously not been any >= 2dimensional manifold for which all the pwidths are known. In recent joint work with Otis Chodosh, we found all pwidths on the round 2sphere and thus the previously unknown Liokumovich–Marques–Neves Weyl law constant in dimension 2. Our work combines Lusternik–Schnirelmann theory, integrable PDE, and phase transition techniques.
Mirror symmetry for log del Pezzo surfaces
Tristan Collins (MIT) October 18, 2021
If X is a del Pezzo surface and D is a smooth anticanonical divisor, we can regard the complement X\D as a noncompact CalabiYau surface. I will discuss a proof of a strong form of the StromingerYauZaslow mirror symmetry conjecture for these noncompact surfaces. It turns out the mirror CalabiYau is a rational elliptic surface (in particular, it has an elliptic fibration onto P^1) with a singular fiber which is a chain of nodal spheres. I will discuss how we can construct special Lagrangian fibrations on these manifolds, as well as moduli of complex and symplectic structures and how hyperKahler rotation allows us to construct an identification of these moduli spaces. This is joint work with A. Jacob and Y.S. Lin.
Asymptotically conical CalabiYau manifolds
Ronan Conlon (UTD) October 25, 2021
Asymptotically conical CalabiYau manifolds are noncompact Ricciflat Kähler manifolds that are modelled on a Ricciflat Kähler cone at infinity. I will present a classification result for such manifolds. This is joint work with HansJoachim Hein (Muenster).
Renormalized Area for 4dimensional Minimal Hypersurfaces of a PoincaréEinstein Space
Aaron Tyrrell (UTD) November 1, 2021
In 1999 Graham and Witten showed that one can define a notion of renormalized area for properly embedded minimal submanifolds of PoincaréEinstein spaces. For even dimensional submanifolds this quantity is a conformal invariant of ambient metric and the submanifold. In 2008 Alexakis and Mazzeo wrote a paper on this quantity for surfaces in a 3dimensional PE manifold, getting an explicit formula and studying its functional properties. We will look at a formula for the renormalized area of a minimal hypersurface of a 5dimensional PoincaréEinstein space.
BiOrderability Techniques and Double Twist Links
Jonathan Johnson (OK State) November 8, 2021
The biorderability of link groups has become a fascinating research topic. In this talk, we will survey some useful tools that have been developed to investigate the biorderability of link complements, including results of LinnellRhemtullaRolfsen, Ito, and KinRolfsen. In particular, we will apply these techniques to the double twist link groups.
A survey of veering triangulations
Henry Segerman (OK State) November 15, 2021
Veering triangulations are combinatorial objects introduced by Agol to describe threemanifolds with pseudoAnosov bundle structures. I’ll describe past work with various coauthors relating veering triangulations to other structures on triangulations: strict angle structures and geometric structures, and in building censuses of veering triangulations. I’ll also talk about ongoing work with Saul Schleimer to extend Agol’s correspondence to manifolds with pseudoAnosov flows, and work with Jason Manning and Saul Schleimer to produce CannonThurston maps from veering triangulations. These include the first examples of CannonThurston maps that do not come, even virtually, from surface subgroups.
Tensor Ranks and Matrix Multiplication Complexity
Hang (Amy) Huang (Texas A&M) November 29, 2021
Tensors are just multidimensional arrays. Notions of ranks and border rank abound in the literature. Tensor decompositions also have a lot of application in data analysis, physics, and other areas of science. I will try to give a colloquiumstyle talk surveying my recent two results about tensor ranks and their application to matrix multiplication complexity. The first result relates different notions of tensor ranks to polynomials of vanishing Hessian. The second one computes the border rank of 3 X 3 permanent. I will also briefly discuss the newest technique we used to achieve our results: border apolarity.