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# Events for April 19, 2017 from General and Seminar calendars

## Number Theory Seminar

**Abstract:** We study tensor powers of rank 1 sign-normalized Drinfeld A-modules, where A is the affine coordinate ring of an elliptic curve. Using the theory of A-motives, we find explicit formulas for the A action of these modules. Then, by developing the theory of vector valued Anderson generating functions, we give formulas for the coefficients of the logarithm and exponential functions associated to these A-modules, as well as formulas for the fundamental period.

## Numerical Analysis Seminar

**Abstract:** In this talk, we present an application of the fast algorithm for isogeometric L2 projections for simulations of the tumor growth. We introduce first the system of PDEs describing the model of the melanoma growth, including tumor cell density, flux, pressure, extracellular and degraded extracellular matrices. We also introduce a discrete L-systems model of the vasculature, that provides an oxygen source to the system. The system is solved using explicit scheme and fast isogeometric L2 projections, utilizing the alternating directions solver. Every ten-time steps of the simulation, we couple our continuous model with the discrete vasculature model. We also discuss shared-memory based parallelization of the isogeometric L2 projections solver, using the GALOIS framework [1]. We conclude the presentation with the two-dimensional numerical results from [2], and preliminary parallel three-dimensional results. [1] Marcin Los, Maciej Wozniak, Maciej Paszynski, Andrew Lenharth, Muhamm Amber Hassaan, Keshav Pingali, IGA-ADS : Isogeometric Analysis FEM using ADS solver, Computers & Physics Communications (2017) in press.DOI:10.1016/j.cpc.2017.02.023 [2] Marcin Los, Maciej Paszynski, Adrian Klusek, Witold Dzwinel, Application of fast isogeometric L2 projection solver for tumor growth simulations, Computer Methods in Applied Mechanics and Engineering, 316 (2017) 1257-1269

## Maxson Lecture Series

**Abstract:** This talk will give an overview of the history of various hard problems in number theory which are used as the basis for cryptosystems. I will survey the evolution of attacks and discuss the upcoming NIST competition to standardize new cryptographic schemes for a post-quantum world. I will present some current proposals for post-quantum systems based on supersingular isogeny graphs of elliptic curves and lattice-based cryptosystems in cyclotomic number fields and give the ideas behind some recent attacks.

**Time:** 1:45PM - 2:45PM

**Location:** BLOC 220

**Speaker:** Nathan Green, Texas A&M University

**Title:** *Tensor powers of rank 1 Drinfeld modules on elliptic curves*

**URL:** *Link*

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Maciej Paszynski, Department of Computer Science, AGH University, Krakow, Poland

**Title:** *Fast isogeometric finite element method solver for melanoma tumor growth simulations*

**Time:** 4:00PM - 5:00PM

**Location:** Blocker 149

**Speaker:** Kristin Lauter, Microsoft Research

**Title:** *Maxson Lecture II: How to Keep your Secrets in a Post-Quantum World*