This is the website for the Math Graduate Student Association and the Math Grad Student Seminar.

The math department now has t-shirts! The design can be viewed here. In addition to the grey shirt, there is a red shirt with white lettering. Shirts are $5 and can be purchased in MW (math tower) 216. Cash only, please, and exact change is appreciated but not usually necessary. Sizes range from small to XXL. The shirts are a 50-50 cotton-polyester blend. The design on the back is the Zassenhaus butterfly. ## Mathematical Research Lectures presented by MGSA (Grad Seminar) All talks will be given in CH 240 at 5:15 pm unless otherwise noted. The talks will last between 40 minutes and an hour. All Ohio State undergraduates and graduate students are welcome to attend!  Fall 2017 Spring 2017 Fall 2016 Past Talks • August 29: Evan Nash The Convex Hull of Two Circles in$\mathbb{R}^3$(click for abstract) This is an algebraic geometry talk, but it is a somewhat unorthodox algebraic geometry talk in that not only do you recognize all the words in the title, but they mean exactly what you think they do. We're really going to be looking at two circles in 3-space and trying to describe the properties of their convex hull. On the way, we'll get a glimpse at some of the algebraic geometry machinery we use to get a perspective on this question. There will be many pretty pictures. • September 26: Yongxiao Lin Bounds for$L$-functions and selected applications (click for abstract) Bounding$L$-functions on the critical line$s=1/2+it$is an important problem in number theory. Given an$L$-function$L(s,f)$, from the functional equation and the Phragmen-Lindel\"of principle, we have an upper bound for the order of magnitude of$L(s,f)$on the critical line, which is referred as the convexity bound. The subconvexity problem consists in seeking an upper bound for$L(s,f)$that is superior to the convexity bound by a power saving. In this talk, I will begin with the Lindel\"o hypethesis for the Riemann zeta function. Then we shall talk about subconvexity bounds for degree 2$L$-functions, in various aspects. Applications to the equidistribution of lattice points on the sphere and to arithmetic quantum unique ergodicity (AQUE) will also be discussed. Time permitting, I will mention my own work in this direction for certain degree 3$L$-functions. • October 24: Marissa Renardy A method for parameter sensitivity analysis and parameter estimation using polynomial surrogates (click for abstract) Many mathematical models arising in biology are systems of differential equations with a large number of unknown parameters. Parameter sensitivity analysis and parameter estimation are important tools for understanding these systems. Most methods for this type of parameter analysis require sampling of the parameter space, which becomes very costly as the dimension of the parameter space increases since each sample requires the solution of a system of differential equations. In this talk, I will present a method for parameter sensitivity analysis and parameter estimation that makes use of polynomial surrogate models to greatly reduce the computational cost. I will also demonstrate the method on two models for cell polarization. • November 7: Alex Beckwith The spectral theory of automorphic forms (click for abstract) Automorphic forms are one of the central objects of study in modern analytic number theory. In our setting, they arise as eigenfunctions of the Laplacian on hyperbolic surfaces$\Gamma \backslash \mathbb{H}$, where$\Gamma$is a certain kind of subgroup of$SL_2(\mathbb{R})$. I will present the spectral theory of automorphic forms and discuss some of the outstanding questions about them. These include the prevalence (or lack thereof) of Maa$\ss$cusp forms and also the (unique) equidistribution of their mass at high energy levels; both of these features can be studied using$L\$-functions.

• November 28: Reeve Garrett

Research area: Commutative Algebra and Ideal Theory (click for abstract)

Abstract forthcoming.

## Happy Hour

Happy hour schedule forthcoming!

Everyone is welcome to come, drinkers and non-drinkers alike!

Kevin Nowland
MGSA President
nowland.159 (at) osu.edu

Evan Nash
MGSA Treasurer
nash.228 (at) osu.edu

Reeve Garrett
MGSA Vice-President
garrett.425 (at) osu.edu