Colloquium: Marion Campisi (SJSU) @ Keller 401
Oct 18 @ 3:30 pm – 4:30 pm

Title: Analysis of partisan gerrymandering tools in advance of the US 2020 census

Abstract: Over the last decade, mapmakers have precisely gerrymandered political districts for the benefit of their party. In response, political scientists and mathematicians have more extensively investigated tools to quantify and understand the mathematical structure of redistricting problems. Two primary tools for determining whether a particular redistricting plan is fair are partisan-gerrymandering metrics and stochastic sampling algorithms. In this work we explore the Declination, a new metric intended to detect partisan gerrymandering. Within out analyses, we show that Declination cannot detect all forms of packing and cracking, and we compare the Declination to the Efficiency Gap. We show that these two metrics can behave quite differently, and give explicit examples where that occurs.

Applied Math Seminar: Nicolette Meshkat (Santa Clara University) @ Keller 402
Oct 23 @ 3:30 pm – 4:30 pm

Title: Structural Identifiability of Biological Models

Abstract: Parameter identifiability analysis addresses the problem of which unknown parameters of a model can be determined from given input/output data. If all of the parameters of a model can be determined from data, the parameters and the model are called identifiable. However, if some subset of the parameters can not be determined from data, the model is called unidentifiable. We examine this problem for the case of perfect input/output data, i.e. absent of any experimental noise. This is called the structural identifiability problem. We show that, even in the ideal case of perfect input/output data, many biological models are structurally unidentifiable, meaning some subset of the parameters can take on an infinite number of values, yet yield the same input/output data. In this case, one attempts to reparametrize the model in terms of new parameters that can be determined from data. In this talk, we discuss the problem of finding an identifiable reparametrization and give necessary and sufficient conditions for a certain class of linear compartmental models to have an identifiable reparametrization. We also discuss finding classes of identifiable models and finding identifiable submodels of identifiable models. Our work uses graph theory and tools from computational algebra. This is joint work with Elizabeth Gross and Anne Shiu.

Colloquium: Marissa Loving (Georgia Tech) @ Keller Hall 401
Oct 29 @ 4:00 pm – 5:00 pm

Title: Symmetries of Surfaces

Abstract: There are many ways to study surfaces: topologically, geometrically, dynamically, algebraically, and combinatorially, just to name a few. We will touch on some of the motivation for studying surfaces and their associated mapping class groups, which is the collection of symmetries of a surface. We will also describe a few of the ways that these different perspectives for studying surfaces come together in beautiful and sometimes unexpected ways.

PhD defense for Don Krasky @ Keller 401
Nov 6 @ 3:00 pm – 5:00 pm
Colloquium: Elijah Liflyand (Bar-Ilan University) @ Keller 401
Nov 27 @ 3:30 pm – 4:30 pm

Speaker: Elijah Liflyand (Bar-Ilan University)
Title: A tale of two Hardy spaces

New relations between the Fourier transform of a function of bounded
variation and the Hilbert transform of its derivative are revealed.
If we do not distinguish between the cosine and sine transforms and consider
the general Fourier transform of $f$, direct calculations give the belonging
of the derivative $f’$ to the real Hardy space $H^1$ as a sufficient condition
for the integrability of the Fourier transform. Our analysis is more delicate.
The main result is an asymptotic formula for the {bf cosine} Fourier
transform, while much earlier known results gives an asymptotic formula
for the sine Fourier transform. The difference is achieved by assuming that
the derivative belongs to different subspaces of $H^1$. However, this tale of
each of the two subspaces were impossible if we would not have a new proof
even for the old result. The known proofs used to give strong priority just to
the sine transform. Interrelations of various function spaces are studied
in this context, first of all of these two types of Hardy spaces. The obtained
results are used for proving completely new results on the integrability
of trigonometric series.

Colloquium: Nate Brown (Penn State)
Dec 6 @ 3:30 pm – 4:30 pm

Speaker: Nate Brown (Penn State)

Title: Tomorrow’s STEM leaders are diverse

Abstract: Thirty years ago a radical experiment began at the University of Maryland Baltimore County (UMBC). The aim was to prepare undergraduates from underrepresented groups to be successful graduate students in STEM fields. The pillars of the program were unorthodox and the results have been stunning. In this talk I will discuss the Driving Change Initiative, funded by the Howard Hughes Medical Institute, which aims to replicate UMBC’s experiment at research institutions across the country.

Colloquium: Prasit Bhattacharya (U. Virginia) @ Keller 301
Dec 20 @ 2:30 pm – 3:30 pm

Speaker: Prasit Bhattacharya (U. Virginia)

Title: Stable homotopy groups of spheres, finite CW-complexes and periodic self-maps

Abstract: Patterns in the stable homotopy groups of spheres are hard to detect. However chromatic homotopy theory gives a theoretical framework which justifies existence of a robust pattern. In theory, elements of stable homotopy groups are arranged in layers called the chromatic layers (one for each natural number). However, not much is known beyond chromatic layer 1. One way to detect elements in the stable homotopy groups is via finite CW-complexes which admit special self-maps, called v_n-self-maps. This talk will introduce a new class of CW-complexes which has the potential to detect elements in chromatic layer 2 of the stable homotopy group localized at the prime 2.

Colloquium: Anna Puskas (Kavli Institute) @ Keller 401
Jan 22 @ 3:30 pm – 4:30 pm

Speaker: Anna Puskas (Kavli Institute for the Physics and Mathematics of the Universe)

Title: Demazure-Lusztig operators and Metaplectic Whittaker functions


The study of objects from Number Theory such as metaplectic Whittaker
functions has led to surprising applications of Combinatorial
Representation Theory. Classical Whittaker functions can be expressed in
terms of symmetric polynomials, such as Schur polynomials via the
Casselman-Shalika formula. Tokuyama’s theorem is an identity that links
Schur polynomials to highest-weight crystals, a symmetric structure that
has interesting combinatorial parameterizations.

Approaches to generalizing the Casselman-Shalika formula resemble the
two sides of Tokuyama’s identity. Connecting these approaches with
purely combinatorial tools motivates the search for a generalization of
Tokuyama’s theorem. This talk will discuss how the introduction of
certain algebraic tools (Demazure and Demazure-Lusztig operators) yields
such a result. We shall see how these tools can further be used to
investigate questions in the infinite-dimensional setting.