### This Week in Mathematics

 Monday February 20, 2017 Profs talk just for students [url]     - Mark van Hoeij, FSU MathTime: 2:30 Room: 200 LOVAbstract/Desc: Professors talk about their research interests and expertise; after the short talks they invite students with interest to come to their offices to chat further. PURE and ACM graduate students in their first year may be enrolled as mat5933. Tuesday February 21, 2017 Applied PDE seminar Numerical simulation of evolution equations using the spectral renormalization method    - Ziad Musslimani, Florida State UniversityTime: 4:30-5:20 Room: LOV227 Wednesday February 22, 2017 Departmental Tea Time C is for cookie, and shorthand for C[0,1] w/the sup normTime: 3: Room: 204 LOV Profs talk just for students [url]     - Eric Klassen, FSU MathTime: 2:30 Room: 200 LOVAbstract/Desc: Professors talk about their research interests and expertise; after the short talks they invite students with interest to come to their offices to chat further. PURE and ACM graduate students in their first year may be enrolled as mat5933. Biomathematics Seminar [url] Bacteria Motility in Variable-Viscosity Environments    - Patrick Eastham, Florida State UniversityTime: 3:35 pm Room: 107 LOV Thursday February 23, 2017 Joint Mathematics-GFDI Colloquium [url] New Strategies for Reduced-Order Models for Predicting the Statistical Responses and Uncertainty Quantification in Complex Turbulent Dynamical Systems    - Andrew Majda, Courant Institute, New York UniversityTime: 4:00 pm Room: Keen 7th floor conference roomMore Information Financial Mathematics Seminar Discrete Sums of Geometric Brownian Motions, Annuities and Asian Options    - Lingjiong Zhu, Time: 3:35pm Room: 201 LovAbstract/Desc: The discrete sum of geometric Brownian motions plays an important role in modeling stochastic annuities in insurance. It also plays a pivotal role in the pricing of Asian options in mathematical finance. We study the probability distributions of the infinite sum of geometric Brownian motions, the sum of geometric Brownian motions with geometric stopping time, and the finite sum of the geometric Brownian motions. We derive tail asymptotics and compute numerically the asymptotic distribution function. We compare the results against the known results for the continuous time integral of the geometric Brownian motion up to an exponentially distributed time. The results are illustrated with numerical examples for life annuities with discrete payments, and Asian options. This is based on the joint work with Dan Pirjol. Algebra and its applications [url] Rational Surface Automorphism: Homology actions of real mappings    - Kyounghee Kim, FSUTime: 3:35 pm Room: 104 LOVAbstract/Desc: Let $$f:X \to X$$ be a quadratic rational surface automorphism fixing a cuspidal cubic. Let $$X_R$$ be the closure of the $$\mathbb{RP}^2$$ inside $$X$$. When the multiplier at the invariant cuspidal cubic is real, $$f$$ induces the automorphism $$f_R$$ of $$X_R$$. In this talk, we will discuss the homology action of $$f_R$$ and and the real mappings with maximal entropy. Friday February 24, 2017 Colloquium Tea Time: 3:00 pm Room: 204 LOV Applied PDE seminar (joint with GFDI seminar) Simple Stochastic Dynamical Models Capturing the Statistical Diversity of El Nino Southern Oscillation    - Nan Chen, Courant Institute, New York UniversityTime: 11:00-11:50 Room: Keen 18Abstract/Desc: The El Nino Southern Oscillation (ENSO) has significant impact on global climate and seasonal prediction. A simple modeling framework is developed here that automatically captures the statistical diversity of ENSO. First, a stochastic parameterization of the wind bursts including both westerly and easterly winds is coupled to a simple ocean-atmosphere model that is otherwise deterministic, linear and stable. Secondly, a simple nonlinear zonal advection with no ad-hoc parameterization of the background sea surface temperature (SST) gradient and a mean easterly trade wind anomaly representing the multidecadal acceleration of the trade wind are both incorporated into the coupled model that enable anomalous warm SST in the central Pacific. Then a three-state stochastic Markov jump process is utilized to drive the wind burst activity that depends on the strength of the western Pacific warm pool in a simple and effective fashion. It allows the coupled model to simulate the quasi-regular moderate traditional El Nino, the super El Nino, the central Pacific (CP) El Nino as well as the La Nina with realistic features. In addition to the anomalous SST, the Walker circulation anomalies at different ENSO phases all resemble those in nature. In particular, the coupled model succeeds in reproducing the observed episode during 1990s, where a series of 5-year CP El Nino is followed by a super El Nino and then a La Nina. Importantly, both the variance and the non-Gaussian statistical features in different Nino regions spanning from the western to the eastern Pacific are captured by the coupled model.