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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 […]

GEMS Workshop: Mathematics of Information with Professor Lucas Bang of Harvey Mudd College

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

TOPIC: The Mathematics of Information We are surrounded by information. Words in books, ones and zeros in computers, mathematical equations, and DNA sequences are all examples of information, but can we say something more about it? In this workshop, we will learn about the mathematics of information, see how it is related to concepts from […]

Markov Chains and Emergent Behavior in Programmable Matter given by Prof. Sarah Canon (CMC)

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

Markov chains are widely used throughout mathematics, statistics, and the sciences, often for modelling purposes or for generating random samples. In this talk I’ll discuss a different, more recent application of Markov chains, to developing distributed algorithms for programmable matter systems. Programmable matter is a material or substance that has the ability to change its […]

Differential spectra of power permutations (Daniel Katz, CSUN)

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

If $F$ is a finite field and $d$ is a positive integer relatively prime to $|F^\times|$, then the power map $x \mapsto x^d$ is a permutation of $F$, and so is called a power permutation of $F$. For any function $f: F \to F$, and $a, b \in F$, we define the differential multiplicity of $f$ with respect to […]

Paper Strip Knots (David Bachman)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

I will discuss joint work with Jim Hoste, where we prove that a unique folded strip of paper can follow any polygonal knot with odd stick number. In the even stick number case there are either infinitely many, or none.

Science for the Greater Good: How a Math Professor Saved the Italian Coastline from Big Oil

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

In 2007, Dr. Maria D'Orsogna learned of proposed oil activities in her home region of Abruzzo, Italy. Century-old wineries were to be uprooted to build clusters of oil wells, refineries and pipelines, turning scenic Abruzzo into an oil district. Although based in California, 6,000 miles away, Dr. D'Orsogna took it upon herself to raise awareness […]