Department of Mathematics

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Abstracts

Week of September 11, 2022

September 12, 2022
Applied Mathematics	Metric representations: Algorithms and Geometry	3:00pm - AKW 200	Abstract: Given a set of distances amongst points, determining what metric representation is most “consistent” with the input distances or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. In this talk, we discuss a number of variants of this problem, from convex optimization problems with metric constraints to sparse metric repair. Bio: Anna C. Gilbert is Professor of Mathematics and Statistics and Data Science. Gilbert received her Bachelor of Science degree from the University of Chicago and a Ph.D. from Princeton University, both in Mathematics. In 1997, she was a postdoctoral fellow at Yale University and AT&T Labs-Research. From 1998 to 2004, she was a member of technical staff at AT&T Labs-Research in Florham Park, NJ. From 2004 to 2020, she was with the Department of Mathematics (with a secondary appointment in Electrical and Computer Engineering) at the University of Michigan, where she was appointed the Herman H. Goldstine Collegiate Professor. In 2020, she joined Yale University as the John C. Malone Professor of Mathematics and Professor of Statistics & Data Science. She has received several awards, including a Sloan Research Fellowship (2006), an NSF CAREER award (2006), the National Academy of Sciences Award for Initiatives in Research (2008), the Association of Computing Machinery (ACM) Douglas Engelbart Best Paper award (2008), the EURASIP Signal Processing Best Paper award (2010), and the SIAM Ralph E. Kleinman Prize (2013). Her research interests include analysis, probability, discrete mathematics, and algorithms. She is especially interested in randomized algorithms with applications to harmonic analysis, signal and image processing, and massive datasets.
Group Actions, Geometry and Dynamics	Rigidity of Kleinian groups via self-joinings	4:00pm - LOM 206	Discrete subgroups of $\rm{PSL}_2(\mathbb C)$ are called Kleinian groups. Mostow rigidity theorem (1968) says that Kleinian groups of finite co-volume (=lattices) do not admit any faithful discrete representation into $\rm{PSL}_2(\mathbb C)$ except for conjugations. I will present a new rigidity theorem for finitely generated Kleinian groups which are not necessarily lattices, and explain how this theorem compares with Sullivan’s rigidity theorem (1981). This talk is based on joint work with Dongryul Kim.
Geometry, Symmetry and Physics	GW/FJRW correspondence and Stokes phenomenon for non Calabi-Yau hypersurfaces	4:30pm - LOM 214	Abstract: The study of Landau-Ginzburg/Calabi-Yau correspondence using linear sigma models was proposed by Witten in the early 90's of last century. A mathematical version of the correspondence using curve-counting theories has been realized by Chiodo, Ruan, Iritani, and many other people in the past decade. Namely, there is an equivalence between counting stable maps in the CY hypersurface of a weighted polynomial W (i.e. Gromov-Witten theory of the hypersurface) and counting $W$-spin structures (i.e. Fan-Jarvis-Ruan-Witten theory of W). So LG/CY correspondence can be realized as GW/FJRW correspondence. I will talk about a generalization of such a GW/FJRW correspondence for non-CY hypersurfaces. A key ingredient here is the Gamma structures developed by Iritani, and Katzarkov-Kontsevich-Pantev. For Fano manifolds, Galkin-Golyshev-Iritani's Gamma conjectures predict the Gamma class of the quantum cohomology equals the asymptotic class from an irregular meromorphic connection. The irregular Riemann-Hilbert correspondence of the connection generates Stokes phenomenon. We can view the FJRW theory as a part of the GW theory in the Stoke decomposition. The similar phenomenon works for hypersurfaces of general type as well, where the GW theory is viewed as a part of the FJRW theory. Our GW/FJRW correspondence is compatible with Orlov's semi-orthogonal decomposition.

September 13, 2022
Geometry & Topology	Convex cocompact subgroups of the Goeritz group	4:15pm - LOM 214	This talk is about hyperbolicity of surface group extensions and a question of Farb-Mosher about whether purely pseudo-Anosov subgroups of mapping class groups are convex cocompact. We’ll explain this problem and give an answer for subgroups of the genus-2 Goeritz group, which is the group of mapping classes of a genus-2 surface that extend to the genus-2 Heegaard splitting of the 3-sphere. In addition we give a refined version of the Nielsen-Thurston classification for the Goeritz group.

September 15, 2022
Algebra and Geometry lecture series	Cohomology of Hitchin moduli spaces and the P=W conjecture.	4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214

September 16, 2022
Friday Morning Seminar	Friday Mornings	10:30am - LOM 205	Please join our relaxed-paced seminar on impromptu subjects relating to the interests of our audience. Everyone from all backgrounds are welcome. The subjects are mostly geometry, probability, combinatorics, dynamics and more! Hope to see you there!