## Colloquia

Colloquia for the Department of Mathematics and Statistics are normally held in **University Hall 4010 on Fridays at 4:00 p.m.** Any departures from this are indicated below. Light refreshments are served before
the colloquia in 2040 University Hall. Driving directions, parking information and maps are available on the university website.

## 2019-2020 Colloquia

Below is a list of speakers, talk titles and abstracts for the current academic year. Abstracts for the talks are also posted in the hallways around the departmental offices.

**Spring Semester **

**April 21-24, 2020 (Postponed)**

Pasha Etingof (Massachusetts Institute of Technology)

**April, 2020 (Postponed)**

Brian J. Parshall (University of Virginia)

**April 3, 2020 (Postponed)**

James Broda (Bowdoin College)

**March 26, 2020 (Postponed)**

Van Vu (Yale)

**March 20, 2020 (Postponed)**

Peter Miller (University of Michigan)

**March 6, 2020**

Meera Mainkar (Central Michigan) *Preserve one, Preserve all*

Abstract: The classical Beckman-Quarles theorem states that a self map on a Euclidean $n$-space ($n \ge 2$) which preserves the length 1 must be an isometry. We formulate and prove cases of a conjecture stating that if $X$ is a complete Riemannian manifold (dim $X \ge 2$), then a self map on $X$ which preserves sufficiently small length is an isometry. This is joint work with Benjamin Schmidt.

**February 28, 2020**

Thomas Koberda (University of Virginia) *Group actions on manifolds and regularity*

Abstract: I will survey some classical results about finitely generated groups acting on manifolds, concentrating on manifolds in dimension one. I will then discuss how the algebraic structure of groups acting on manifolds is affected by regularity considerations. I will concentrate on naturally occurring classes of groups such as nilpotent groups, right-angled Artin groups, and mapping class groups. I will finish with some indications about phenomena in higher dimensions.

**February 21, 2020**

Song Qian (University of Toledo) *Statistical Issues and Solutions of ELISA*

Abstract: The use of a calibration curve in analytical chemistry is common. I Googled the term "calibration curves in chemistry" and found over 13 million results. In practice, a calibration curve is often a regression model based on data from a limited number of standard solutions. A regression model fit to small sample size is known to have a high level of prediction uncertainty (i.e., low measurement accuracy). Furthermore, a commonly used calibration curve plots the concentration on the x-axis and the absorbance on the y-axis. That is, the concentration variable is the predictor and the absorbance is the response variable. A regression model minimizes the model "error" with respect to the response variable. Consequently, measurement accuracy is lower than the model statistics suggest. Using data from Ohio EPA's drinking water cyanobacterial toxin (microcystin) monitoring program, I discuss sources of uncertainty in a typical process of measuring microcystin concentration using the calibration curve embedded in the ELISA kit. The presentation focuses on a proposed statistical solution. Based on my preliminary result, the statistical solution can reduce the measurement uncertainty by an order of magnitude (based on standard deviations of a simulation study). I developed a software package that can be shared and executed in the cloud (Google Colab). As a result, the new method will not require changes in current analytical practices.

**February 14, 2020**

Stephen Rush (Bowling Green State University) *Measuring Information Asymmetry in Event Time*

Abstract: I describe the importance of using event time in measure information asymmetry in U.S. equity markets. Information asymmetry between market participants represents a risk that is compensated by a higher expected return for both short-term traders and long-term investors. Firms with greater information asymmetry have higher expected returns and lower prices while firms with lower information asymmetry have lower expected returns and higher prices. A long/short trading strategy built on these results produces abnormal returns of 11.45% per year.

**January 31, 2020**

Michael Shapiro (Michigan State) *Noncommutative Pentagram Map*

Abstract: A pentagram map is a discrete integrable transformation on the space of projective classes of (twisted) n-gons in projective plane. We will discuss a classical and non-commutative version of pentagram map and its integrability properties.

**Fall Semester**

**December 6, 2019**

Michael Gekhtman (University of Notre Dame) *Five Glimpses of Cluster Algebras*

Abstract: Cluster algebras were introduced by Fomin and Zelevinsky almost 20 years ago and have since found exciting applications in many areas including algebraic geometry, representation theory, integrable systems and theoretical physics. I will use examples to explain a definition of a cluster algebra and then sketch several applications of the theory, including Somos-5 recursion, pentagram map and generalizations of Abel's pentagon identity

**November 8, 2019**

Pavel Mnev (University of Notre Dame) *Batalin-Vilkovisky formalism: an example*

Abstract: I will explain the Batalin-Vilkovisky formalism in an interesting explicit example, where one associates to a unimodular differential graded Lie V algebra a space of fields with an action function on it (satisfying certain PDE - the "quantum master equation"). Then, by computing a certain fiber integral, one produces an induced (or "homotopy-transferred") algebraic structure on a subcomplex of V. Applying the construction to the algebra of differential forms on a manifold, one gets an interesting induced algebraic structure on cochains of a triangulation. In the case of an interval, this is a unimodular $L_.$ structure with structure constants of the operations given by Bernoulli numbers.

**October 25, 2019**

Benjamin Ward (Bowling Green State University) *Rational homotopy type of moduli spaces*

Abstract: Our favorite algebraic operations are associative, but the property of associativity doesn't always mix well with homotopy theory. In the first part of this talk I will review an analog of associativity which is homotopy invariant, and indicate how this notion may be used to study topological spaces. I will then explain how these techniques can be adapted to study families of spaces which can be glued together along graphs, and focus on the example of moduli spaces of punctured surfaces.

**October 18, 2019**

Robert Clark *An overview of data related skills and an example of their application on an organization*

Abstract: Today the world's most valuable resource is no longer oil, but data. In this discussion the presenter will summarize the necessary data skills that are required to be a productive resource for an organization, how an organization utilizes these resources and a use case on how Risk is descriptively, predictively and prescriptively evaluated at scale for an organization.