• Speaker: Sarah Klanderman, MSU
• Title: Computations in Topological CoHochschild Homology
• Date: 11/18/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

Hochschild homology (HH) is a classical algebraic invariant of rings that can be extended topologically to be an invariant of ring spectra, called topological Hochschild homology (THH). There exists a dual theory for coalgebras called coHochschild homology (coHH), and in recent work Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology (coTHH). In this talk we will discuss coTHH calculations and the tools needed to do them.

• Speaker: Joshua Ruiter, Michigan State
• Title: Split and non-split tori
• Date: 11/18/2019
• Time: 4:30 PM - 5:30 PM
• Place: C517 Wells Hall

Tori are an important structural aspect of algebraic groups, and "split" vs "non-split" tori are especially important. Unfortunately, "non-split" phenomena only occur over non-algebraically closed fields, so not all the traditional tools of classical algebraic geometry apply. Using the generalized field norm map from my talk last week, I'll describe a concrete example of a non-split torus. Then we'll try to use that example to try and understand the importance of non-split tori.

• Speaker: Brent Nelson, MSU
• Title: Derivations on von Neumann algebras
• Date: 11/19/2019
• Time: 11:30 AM - 12:30 PM
• Place: C304 Wells Hall

In this learning seminar style talk, I will define the notion of a derivation on a von Neumann algebra. I will also discuss their history and how they factor into modern research in operator algebras.

• Speaker: Matthew Hedden, MSU
• Title: Spectral sequence from Khovanov to instanton homology
• Date: 11/19/2019
• Time: 12:00 PM - 1:30 PM
• Place: C117 Wells Hall

No abstract available.

• Speaker: Honghao Gao, MSU
• Title: Applications of augmentations in contact topology
• Date: 11/19/2019
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall

Chekanov introduced a differential graded algebra as an invariant for Legendrian knots in standard contact manifold R^3. An augmentation is a rank 1 representation of the dga. Augmentations are accessible invariants, and the moduli space of augmentations carries important properties from both algebraic and geometric perspectives. In this talk, I will review some problems in contact topology and discuss the applications of augmentations.

• Speaker: Andrey Gogolyev, Ohio State University
• Title: Rigidity for higher dimensional expanding maps
• Date: 11/19/2019
• Time: 3:50 PM - 4:50 PM
• Place: C304 Wells Hall

Expanding maps are self covers of smooth compact manifolds which expand the lengths of all non-zero tangent vectors. Classification of such maps up to topological conjugacy is known due to work of Shub, Franks and Gromov. Classification up to smooth conjugacy should be quite different because periodic points of expanding maps carry invariants of $C^1$ conjugacy. Shub and Sullivan classified expanding maps on the circle up to smooth conjugacy on the circle. I will explain smooth classification of expanding maps in higher dimensions on and open dense set in the space of expanding maps. Joint work with F. Rodriguez Hertz.

• Speaker: Patrick Allen, UIUC
• Title: On the modularity of elliptic curves over imaginary quadratic fields
• Date: 11/20/2019
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

The Langlands-Tunnell theorem is an important starting point in Wiles's proof of the modularity of semistable elliptic curves over the rationals. Over imaginary quadratic fields it is unclear how to similarly use the Langlands-Tunnell theorem and Wiles's strategy runs into problems right from the start. I will motivate and explain the subtle but fundamental issues that arise, and indicate how they can be circumvented in many cases. As an application, we deduce that a positive proportion of elliptic curves over imaginary quadratic fields are modular. This is joint work with Chandrashekhar Khare and Jack Thorne.

• Speaker: Michelle Cirillo, University of Delaware; Jennifer Reed, Odyssey Charter Middle School, Delaware
• Title: Learning Together Through Collaborative Research: The Case of Proof in Secondary Mathematics
• Date: 11/20/2019
• Time: 3:30 PM - 5:00 PM
• Place: 252 EH

The Proof in Secondary Classrooms (PISC) project is a design and development research study focused on secondary students’ success with mathematical proof. The goal of this project was to develop a new and improved intervention to support the teaching and learning of proof. The central research objective of this project was to develop a pedagogical framework and a corresponding set of lesson plans and support materials to guide teachers toward improving students’ success with proof. The primary educational objective of this project was to support mathematics educators in understanding particular sub-goals of proof and developing strategies for teaching them. We present data and findings from our three-year collaboration on this project (2016-2019), which made use of ideas from design research and lesson study, and we discuss lessons learned through our collaboration.

• Speaker: Kari Eifler, Texas A&M University
• Title: The graph isomorphism game for quantum graphs
• Date: 11/21/2019
• Time: 11:30 AM - 12:30 PM
• Place: C304 Wells Hall

Non-local games give us a way of observing quantum behaviour through the observation of only classical data. The graph isomorphism game is one such non-local game played by Alice and Bob which involves two finite, undirected graphs. A winning strategy for the game is called quantum if it utilizes some shared resource of quantum entanglement between the players. We say two graphs are quantum isomorphic if there is a winning quantum strategy for the graph isomorphism game. We show that the *-algebraic, C*-algebraic, and quantum commuting (qc) notions of a quantum isomorphism between classical graphs X and Y are all equivalent. This is based on joint work with M. Brannan, A. Chirvasitu, S. Harris, V. Paulsen, X. Su, and M. Wasilewski.

• Speaker: Leonardo Abbrescia, MSU
• Title: Stability of traveling planewave solutions to Lorentzian vanishing mean curvature flow
• Date: 11/21/2019
• Time: 1:00 PM - 1:50 PM
• Place: C517 Wells Hall

Lorentzian minimal submanifolds of Minkowski space are the dynamic analogue of minimal surfaces in the elliptic regime. They are defined by the vanishing of mean curvature, which can be expressed as a system of geometric PDEs. With the requirement that the submanifold be Lorentzian, that is, that the induced metric is Lorentzian, the equations have a hyperbolic nature. Consequently, the natural approach to study them is via the Cauchy initial value problem. In this talk we discuss stability properties of traveling planewave solutions to these equations, and highlight the difficulties introduced by the "infinite energy" planewave background. This is joint work with Willie Wong.

• Speaker: Akram Alishahi, University of Georgia
• Title: Braid invariant relating knot Floer homology and Khovanov homology
• Date: 11/21/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

Khovanov homology and knot Floer homology are two knot invariants that were defined around the same time, and despite their different constructions, share many formal similarities. After reviewing the construction of Khovanov homology and some of these similarities, we will discuss an algebraic braid invariant which is closely related to both Khovanov homology and the refinement of knot Floer homology into tangle invariants. This is a joint work with Nathan Dowlin.

• Speaker: Craig Gross, Rachel Domagalski, MSU
• Title: Git/Github and Zotero Workshop
• Date: 11/21/2019
• Time: 4:00 PM - 5:00 PM
• Place: C204 Wells Hall

The AMS Grad Student Chapter is putting on a Git, GitHub, and Zotero workshop. If you want to know more about version control / staying organized / making .bib files / best collaboration practices, this workshop is for you! Please bring your laptop. Snacks will be provided!

• Speaker: Exchange Program and MSU Student Research Teams
• Title: Undergraduate MTH and STT Research Project Presentations
• Date: 11/22/2019
• Time: 3:30 PM - 7:00 PM
• Place: C304 Wells Hall

Special event: Undergraduate MTH and STT Research Project Presentations Exchange Program and MSU Student Research Teams will present the results of their research projects

• Speaker: Yeonhyang Kim, Central Michigan University
• Title: Q-ball imaging using predicted diffusion gradient directions
• Date: 11/22/2019
• Time: 4:10 PM - 5:00 PM
• Place: A203 Wells Hall

We review the theory of q-ball imaging and describe a simple linear matrix formulation for the q-ball reconstruction based on spherical harmonic basis function interpolation. In this talk, we present a novel method to improve the q-ball reconstruction by determining appropriate positions at which a synthesized signal is obtained by combining surrounding signals in given diffusion gradient directions.