• Speaker: Peikai Qi, MSU
• Title: Iwasawa lambda-invariants and Massey products
• Date: 02/20/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Preston Wake (wakepres@msu.edu)

No abstract available.

• Speaker: Ian Montague , Brandeis University
• Title: Seiberg-Witten Floer K-Theory and Cyclic Group Actions
• Date: 02/21/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

Given a spin rational homology sphere equipped with a cyclic group action, I will introduce equivariant refinements of Manolescu's kappa invariant, derived from the equivariant K-theory of the Seiberg--Witten Floer spectrum. These invariants give rise to equivariant relative 10/8-ths type inequalities for equivariant spin cobordisms between rational homology spheres. I will explain how these inequalities provide applications to knot concordance, obstruct cyclic group actions on spin fillings, and give genus bounds for knots in punctured 4-manifolds. If time permits I will explain how these invariants are related to equivariant eta-invariants of the Dirac operator, and describe work-in-progress which provides explicit formulas for the $S^1$-equivariant eta-invariants on Seifert-fibered spaces.

• Speaker: Francis Bonahon, MSU
• Title: The quantum trace for skein algebras of surfaces
• Date: 02/21/2023
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall
• Contact: Michael Shapiro (mshapiro@msu.edu)

The quantum trace homomorphism connects two competing quantizations for the $SL_n$-character variety of a surface, consisting of $SL_n$-local systems over the surface. The first quantization is through the $SL_n$-skein algebra, which is intrinsic but difficult to work with. The second quantization is based on a quantization of Thurston-Fock-Goncharov local coordinates, and is algebraically easier to handle but depends on choices. I will focus on the construction of this quantum trace in the case where $n=2$.

• Speaker: Himchan Jeong, Department of Statistics and Actuarial Science at Simon Fraser University in Canada
• Title: Integration of Traditional and Telematics Data for Efficient Insurance Claims Predictions
• Date: 02/21/2023
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Amanda Nickols (nickols2@msu.edu)

Linked Abstract

While driver telematics has gained attention for risk classification in auto insurance, scarcity of observations with telematics features has been problematic, which could be owing to either privacy concern or adverse selection compared to the data points with traditional features. To handle this issue, we propose a data integration technique based on calibration weights. It is shown that the proposed technique can efficiently integrate the so-called traditional data and telematics data and also cope with possible adverse selection issues on the availability of telematics data. Our findings are supported by a simulation study and empirical analysis on a synthetic telematics dataset.

• Speaker: Hemanshu Kaul, Illinois Institute of Technology
• Title: Polynomials and DP-coloring of Graphs
• Date: 02/22/2023
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

DP-coloring (also called correspondence coloring) of graphs is a generalization of list coloring of graphs that has been widely studied in recent years after its introduction by Dvorak and Postle in 2015. Intuitively, DP-coloring is a variation on list coloring where each vertex in the graph still gets a list of colors, but identification of which colors are different can change from edge to edge. DP-coloring has been investigated from both the extremal (DP-chromatic number) and the enumerative (DP-color function) perspectives. In this talk, we will give an overview of questions arising with regard to when the DP-color function equals the chromatic polynomial (or any polynomial), and how the polynomial method, through the Combinatorial Nullstellensatz and the Alon-Furedi theorem for the number of non-zeros of a polynomial, can be applied to both extremal and enumerative problems in DP-coloring. Many open problems and conjectures will be presented.

• Speaker: Konstantinos Kavvadias , University of Cambridge
• Title: Conformal removability of SLE_4
• Date: 02/22/2023
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Dapeng Zhan (zhan@msu.edu)

We consider the Schramm-Loewner evolution (SLE_kappa) with kappa=4, the critical value of kappa>0 at or below which SLE_kappa is a simple curve and above which it is self-intersecting. We show that the range of an SLE_4 curve is a.s. conformally removable, answering a question posed by Sheffield. In order to establish this result, we give a new sufficient condition for a set X in the complex plane to be conformally removable which applies in the case that X is not necessarily the boundary of a simply connected domain. This is based on a recent joint work with Jason Miller and Lukas Schoug.

• Speaker: Igor Rapinchuk, MSU
• Title: Cancelled: Profinite groups and infinite Galois theory
• Date: 02/22/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

No abstract available.

• Speaker: Pavel Coupek, MSU
• Title: Property(Pr) and completed tensor product
• Date: 02/23/2023
• Time: 2:10 PM - 3:10 PM
• Place: C204A Wells Hall
• Contact: Peikai Qi (qipeikai@msu.edu)

No abstract available.

• Speaker: Yufeng Liu, University of North Carolina at Chapel Hill
• Title: ZOOM TALK (password the smallest prime > 100) - Learning Individualized Treatment Rules with Many Treatments
• Date: 02/23/2023
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Mark A Iwen ()

Learning an optimal Individualized Treatment Rule (ITR) is a very important problem in precision medicine. In this talk, we consider the challenge when the number of treatment arms is large, and some groups of treatments in the large treatment space may work similarly for the patients. Motivated by the recent development of supervised clustering, we propose a novel adaptive fusion-based method to cluster the treatments with similar treatment effects together and estimate the optimal ITR simultaneously through a single convex optimization. We establish the theoretical guarantee of recovering the underlying true clustering structure of the treatments for our method. Finally, the superior performance of our method will be demonstrated via both simulations and a real data application on cancer treatment. This is joint work with Haixu Ma and Donglin Zeng at UNC-Chapel Hill.

• Speaker: Zhenqi Wang, Michigan State University
• Title: Periodic data and smooth rigidity for hyperbolic automorphisms on torus
• Date: 02/23/2023
• Time: 3:00 PM - 4:00 PM
• Place: A126 Wells Hall
• Contact: Fan Yang (yangfa31@msu.edu)

We study the regularity of the conjugacy between an irreducible Anosov automorphism $A$ on torus and its small perturbation $f$. We say that $f$ and $A$ has the same periodic data if the derivatives of the return maps of $f$ and $A$ at the corresponding periodic points are conjugate. We demonstrate that if $f$ is a $C^s$ diffeomorphism with $s$ sufficiently large and has the same periodic data as $A$, then the conjugacy is $C^{s-\epsilon}$. This completes the characterization of the most elementary $C^1$-invariant for local smooth rigidity. We also give the first example of cocycle rigidity over fibers with conjugate periodic data.

• Speaker: Brendan Hassett, Brown University
• Title: Rationality in families
• Date: 02/23/2023
• Time: 4:10 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Joseph Waldron (waldro51@msu.edu)

A smooth complex projective variety is rational if it can be obtained from projective space by algebraic surgeries, i.e. blowups and blowdowns. It is stably rational if it becomes rational after takinga product with some projective space. Consider a family of such varieties over a connected base. Which members are rational? Stably rational? We focus on recent general results and also outstanding questions that remain. These are illustrated in several key examples, including hypersurfaces of low degree. Joint work with Kresch, Pirutka, and Tschinkel.

• Speaker: Yuehaw Khoo, U Chicago
• Title: New approaches in simulation of transition paths
• Date: 02/24/2023
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Mark A Iwen (iwenmark@msu.edu)

Tensor method can be used for compressing high-dimensional functions arising from partial differential equations (PDE). In this talk, we focus on using these methods for the simulation of transition processes between metastable states in chemistry applications, for example in molecular dynamics. To this end, we also propose a novel generative modeling procedure using tensor-network without the use of any optimization.