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GEMS Workshop: Symmetry with Professor Michael Orrison, from Harvey Mudd College

Shanahan 1480, Harvey Mudd College 301 Platt Blvd., Claremont, CA, United States

TOPIC: Symmetry Symmetry seems to be an important idea in mathematics, but how do mathematicians think about symmetry? In this workshop, we’ll talk about mathematical objects called groups, see how they are used to describe symmetry, and then put them to work to help us answer some nontrivial counting problems. WHAT IS GEMS: The Gateway to […]

Applied Math Seminar: Mathematical model of Hematopoietic cell differentiation from single-cell gene sequencing data (Prof. Heyrim Cho ,UCR)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

Recent advances in single-cell gene sequencing data and high-dimensional data analysis techniques are bringing in new opportunities in modeling biological systems. In this talk, I will discuss different approaches to develop mathematical models from single-cell data. Particularly for high-dimensional single-cell gene sequencing data, dimension reduction techniques are applied to find the trajectories of cell states […]

Matroids: a unified theory of independence (Mauricio Gomez Lopez, University of Oregon)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

In this talk, I will give an overview of the theory of matroids. These are mathematical objects which capture the combinatorial essence of linear independence. Besides providing some basic definitions of this theory, I will discuss several examples of matroids and explain some connections with optimization. Also, in this talk, I will introduce matroid polytopes, […]

Topology Seminar: Mauricio Gomez Lopez (U. Oregon)

Title: Cobordism Categories and Spaces of Manifolds. Abstract: Cobordisms have been one of the central objects in topology since the pioneering work of Rene Thom, which provided the first link between manifolds and homotopy theory. In more recent years, there has been much focus on cobordism categories. These play a fundamental role in the study […]

Formal geometry and characteristic classes

I plan to explain how a purely algebraic technique involving Lie Algebra Cohomology can be used to construct standard characteristic classes of vector bundles and foliations (in fact, it could be tweaked to give most characteristic classes in differential and complex geometry).

Applied Math Talk: A Full Asymptotic Series of European Call Option Prices in the SABR Model with Beta = 1 given by Zhengji Guo (CGU)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model, as well as improve the speed of the calculations. We consider the SABR model (with $\beta=1$) of stochastic volatility, which we analyze by tools from Malliavin Calculus. We follow […]

Sporadic points on modular curves (Ozlem Ejder, Colorado State University)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

A classic and fundamental result in number theory is due to Mordell who proved that the set of points on an elliptic curve defined over a number field forms a finitely generated abelian group; in particular, it has a finite torsion subgroup. An essential tool to study elliptic curves is the modular curves which are […]

Habitat-driven extinctions: insights from spatially implicit ODE models 

Speaker:  Kate Meyer, Cornell University Abstract: Biodiversity underpins ecosystem functioning but continues to decline on a global scale. Among human activities driving this trend, habitat destruction is a leading culprit in local and global extinctions. Simple mathematical models can address important questions surrounding habitat-driven extinctions---for example, which species are at highest risk, how delayed might […]

Applied Math Talk: Dynamics of neuroendocrine stress response given by Prof. Maria Rita D’Orsogna (CSUN)

CGU Math North House

The hypothalamic-pituitary-adrenal (HPA) axis is a neuroendocrine system that regulates numerous physiological processes. Disruptions are correlated with stress-related diseases such as PTSD and major depression. We characterize "normal" and "diseased" states of the HPA axis as basins of attraction of a dynamical system describing the main hormones regulated by the HPA axis. Our model includes […]

Magnitude meets persistence. What happens after?

Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United States

The magnitude is an isometric invariant of metric spaces that was introduced by Tom Leinster in 2010, and is currently the object of intense research, as it has been shown to encode many invariants of a metric space such as volume, dimension, and capacity. When studying a metric space in topological data analysis using persistent […]

Faster point counting for curves over prime power rings (Maurice Rojas, Texas A&M)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

Counting points on algebraic curves over finite fields has numerous applications in communications and cryptology, and has led to some of the most beautiful results in 20th century arithmetic geometry. A natural generalization is to count the number of points over prime power rings, e.g., the integers modulo a prime power. However, the theory behind the latter kind of point […]

Calculus, Real Fewnomials, and P vs NP

Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United States

We review a beautiful 17th century result by the philosopher Rene Descartes: a univariate real polynomial with t monomial terms has no more than t-1 positive roots. We then see how one can prove a generalization that counts roots of two bivariate polynomials (with few monomial terms), using nothing more than basic calculus. In other […]