# CMU Mathematics Department Colloquia

## Spring 2019

### Organizer

• Department of Mathematics Colloquium Speaker Committee
• Because there might be a time delay in updating the webpage, please always check with the committee for the available dates.

### Meeting Times

Refreshments take place 30 minutes prior to the talk.
Typical Colloquium Talks are Thursday, 4:00–4:50pm, in Pearce 227. Refreshments are in Pearce 216.
There might be some talks scheduled on a different day and time. The following table gives the most accurate information for each event.

### Schedule

 Date Speaker Title (Scroll down for Abstract) Remark 1/10/2019 By-Law Discussion By-Law Discussion 225 1/17/2019 1/24/2019 Department Meeting Department Meeting 225 1/31/2019 By-Law Discussion (rescheduled) By-Law Discussion (rescheduled) 225 2/7/2019 Graduate Area Meeting (rescheduled) Graduate Area Meeting (rescheduled) PE 227 2/14/2019 By-law Discussion By-law Discussion PE 225 2/19/2019 Tuesday David Anderson (Ohio State University) Old Formulas For Degeneracy Loci, With A New Twist 2/21/2019 Steven Spallone (Indian Institute of Science Education and Research, Pune, India.) A Chinese Remainder Theorem for Partitions 2/28/2019 Department Meeting Department Meeting 225 3/7/2019 Spring Recess Spring Recess 3/14/2019 225 3/21/2019 Sara Rimer (Argonne National Lab, University of Chicago) Building Smarter, Dynamic, And More Resilient Urban Watersheds 3/28/2019 Department Meeting Department Meeting 225 4/4/2019 4/11/2019 Anita Bright (Portland State University) Special Colloquium in Mathematics Education Reading Between The Lines: The Meta-Messages In Our Mathematics Examples 4/18/2019 4/19/2019 Friday (11:15 am) Bakul Sathaye (Wake Forest University) Boundaries Of Nonpositively Curved Manifolds And Groups PE 226 4/23/2019 Tuesday Krishna Garikipati (Mathematics & Mechanical Engineering, University of Michigan) Special Colloquium in Mathematics Variational System Identification Of The Partial Differential Equations Governing Pattern-Forming Physics 4/25/2019 Department Meeting Department Meeting 225

### Abstracts

Speaker: David Anderson (February 19)
Title: Old Formulas For Degeneracy Loci, With A New Twist
Abstract: A basic problem from the 19th century asks for the degree of the locus of symmetric matrices of bounded rank; answers were given by Schubert and Giambelli. More recently, many extensions of this problem have been considered, including versions coming from symmetric maps of vector bundles, or for vector bundles equipped with a nondegenerate bilinear form. I will discuss ongoing work with William Fulton, in which we allow the bilinear form to be "twisted", so that it takes values in a nontrivial line bundle. The formulas we obtain extend those of Billey-Haiman, Ikeda-Mihalcea-Naruse, and others, and exhibit new connections with algebraic combinatorics.

Speaker: Steven Spallone (February 21)
Title: A Chinese Remainder Theorem for Partitions
Abstract: Given a natural number $t$ and a partition $\lambda$, there is a notion of a "remainder of $\lambda$ upon division by $t$'', called the $t$-core of $\lambda$. Let $s,t$ be relatively prime, and consider the map taking a given $st$-core $\lambda$ to the pair consisting of its $s$-core and $t$-core. The fibres of this map are infinite. More precisely, we have proven that the cardinality of the set of length $k$ members of a given fibre is a quasipolynomial in $k$, of degree $st-s-t$. This is joint work with K. Seethalakshmi.

Speaker: Sara Rimer (March 21)
Title: Building Smarter, Dynamic, And More Resilient Urban Watersheds
Abstract: As storm events become more frequent and intense, urban watersheds and their stormwater networks are becoming stressed beyond their design capacities leading to more frequent and destructive urban flooding events. These system failures are only exacerbated due to infrastructure that is aging, landuse that is continuously changing in response to demographic shifts, and system complexity that only continues to increase. But traditional engineering interventions meant to improve upon these systems are unfavorable as they entail large-scale and cost-prohibitive infrastructure construction, and only provide a static solution to a dynamic and evolving problem. The recent accessibility of low-cost sensors, microcontrollers, and wireless communication technology has made it possible for the existing stormwater networks to be retrofitted with an assortment of cyber-physical technologies that allow for inexpensive, versatile, minimally-invasive, and fully-automated stormwater control interventions (e.g. hydraulic valve operated by cellularly-connected actuator).
This talk will provide an overview of the emerging field of smart stormwater and how cyber-physical technologies are being utilized for system-level control, giving a specific example using sensors for improved and real-time water quality prediction in the Chicago Area Waterway System. Additionally, for these emergent and disruptive technologies to be positively exploited, there exists a need to understand societal interaction with and adoption of them. Thus, this talk will also discuss the coupling of physical and social science computational models to better understand the potential transformation of communities utilizing them.

Speaker: Anita Bright (April 11)
Title: Reading Between The Lines: The Meta-Messages In Our Mathematics Examples
Abstract: What happens when we learn that some of the word choices and examples we use in mathematics may serve to distance, marginalize, or harm our students? Although we may not intend to privilege some students while oppressing others, learning to recognize and acknowledge the ways mathematics examples can carry unintended messages is part of the process of ensuring mathematics is both accessible and equitable for all learners. Thus, drawing from critical theory and feminist epistemologies, and employing critical discourse analysis, this interactive conversation will explore some of the ways our words in mathematics contexts may land upon our students and their families, and encourage discussion around ways to reframe and recast what we write and say in all of our work related to mathematics education.

Speaker: Bakul Sathaye (April 19)
Title: Boundaries of nonpositively curved manifolds and groups
Abstract: The classical notion of curvature, i.e, sectional curvature, was developed by Riemann in the 19th century. Manifolds with nonpositive sectional curvature have been of interest due to the rich interplay between their geometric, topological and dynamical properties. In 1987, Gromov defined a notion of non-positive curvature for the larger class of geodesic metric spaces. I will define the boundary at infinity of these spaces and discuss how it can be used to construct manifolds that are nonpositively curved and yet do not have a Riemannian metric with non-positive sectional curvature. We will then further extend the notion of nonpositive curvature to groups. In the hyperbolic setting, groups with Menger curve boundary are known to be abundant. However, K. Ruane observed in early 2000s that it was not known whether non-hyperbolic groups have Menger curve boundary. I will end by giving the first examples of non-hyperbolic groups that have Menger curve boundary. Part of this is joint work with C. Hruska and M. Haulmark.

Speaker: Krishna Garikipati (April 23)
Title: Variational System Identification Of The Partial Differential Equations Governing Pattern-Forming Physics
Abstract: We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental biology, where pattern formation is central to the development of any multicellular organism, and from materials physics, where phase transitions similarly lead to microstructure. In both these fields there is a collection of nonlinear, parabolic PDEs that, over suitable parameter intervals and regimes of physics, can resolve the patterns or microstructures with comparable fidelity. This observation frames the question of which PDE best describes the data at hand. This question is particularly compelling because knowledge of the governing PDE immediately delivers insights to the physics underlying the systems. While building on recent work that uses stepwise regression, we present advances that leverage the variational framework and statistical tests. We also address the influences of variable fidelity and noise in the data.