# Mathematics

### The recipe for moments of L-functions and characteristic polynomials of random matrices

Sieg Baluyot

In 2005, Conrey, Farmer, Keating, Rubinstein, and Snaith formulated a 'recipe' that leads to precise conjectures for the asymptotic behavior of integral moments of various families of $L$-functions. They also proved exact formulas for moments of...

### Half-Isolated Zeros and Zero-Density Estimates

Kyle Pratt

We introduce a new zero-detecting method which is sensitive to the vertical distribution of zeros of the zeta function. This allows us to show that there are few ‘half-isolated’ zeros. If we assume that the zeros of the zeta function are restricted...

### Negative moments of the Riemann zeta function

Alexandra Florea

I will talk about recent work towards a conjecture of Gonek regarding negative shifted moments of the Riemann zeta function. I will explain how to obtain asymptotic formulas when the shift in the Riemann zeta function is big enough, and how we can...

### RMT statistics in number theory and in quantum chaos

Montgomery's pair correlation conjecture ushered a new paradigm into the theory of the Riemann zeta function, that of the occurrence of Random Matrix Theory statistics, as developed in part by Dyson, into the theory. A parallel development was the...

### Large deviation estimates for Selberg’s central limit theorem, applications, and numerics

Emma Bailey

Selberg’s celebrated central limit theorem shows that the logarithm of the zeta function at a typical point on the critical line behaves like a complex, centered Gaussian random variable with variance $\log\log T$. This talk will present recent...

### The Fyodorov-Hiary-Keating Conjecture

Louis-Pierre Arguin

In 2012, Fyodorov, Hiary & Keating and Fyodorov & Keating proposed a series of conjectures describing the statistics of large values of zeta in short intervals of the critical line. In particular, they relate these statistics to the ones of log...

### A few results and conjectures on some product-ratio correlation functions of characteristic polynomials of beta-Hermite ensembles

Yan Fyodorov

Rank-one non-Hermitian deformations of  tridiagonal beta-Hermite Ensembles have been introduced by R. Kozhan several years ago. For a fixed N and beta>0 the joint probability density of N complex eigenvalues  was shown to have a form of a...

### Stochastic Gradient Descent: where optimization meets machine learning

Rachel Ward

Stochastic Gradient Descent (SGD) is the de facto optimization algorithm for training neural networks in modern machine learning, thanks to its unique scalability to problem sizes where the data points, the number of data points, and the number of...

### Foundations for Learning in the Age of Big Data III

Maria Florina Balcan

Cynthia Rudin