Do you love factoring numbers? Me too. Whether you're helping your little cousin with her algebra homework or trying to crack an RSA cryptosystem, there's nothing quite like the thrill of taking a big number and writing it as a product of smaller numbers. In this talk we present a brief historical overview of some primality tests and factorization methods; we will also develop in more detail the quadratic sieve method developed by Pomerance in the 1980's, which for many years held the record for fastest implementation of a factorization algorithm. We leave the converse question of how to create a large number from several smaller numbers as an exercise to the interested listener.

The Ricci iteration is a discrete analogue of the Ricci flow. According to Perelman, the Kahler-Ricci flow converges to a Kahler-Einstein metric whenever one exists, and it has been conjectured that the Ricci iteration should behave similarly. In joint work with Y. Rubinstein we are able to confirm this conjecture for general Fano manifolds.

n this talk we will characterize the irreducible quasifinite highest weight modules of some subalgebras of the Lie algebra of matrix quantum pseudodifferential operators $N \times N$.

In order to do this, we will first give a complete description of the anti-involutions that preserve the principal gradation of the algebra of $N\times N$ matrix quantum pseudodifferential operators and we will describe the Lie subalgebras of its minus fixed points. We will obtain, up to conjugation, two families of anti-involutions that show quite different results when $n=N$ and $n< N$. We will then focus on the study of the ``orthogonal'' and ``symplectic'' type subalgebras found for case $n=N$, specifically the classification and realization of the quasifinite highest weight modules.

Pearson's Chi-squared test is very widely used in practice and has a long history. The validity with a large number of cells or small expected frequencies has been open for a long time. We provide a solution to this open problem by rigorously establishing a distributional approximation of Pearson's Chi-squared test statistic by using a high-dimensional central limit theorem for quadratic forms of random vectors. We also propose a modified chi-squared statistic with a faster convergence rate and propose the concept of adjusted degrees of freedom. Our procedure is applied to goodness-of-fit test for the social life feeling data and the Rochdale data.

Sen attached to each $p$-adic Galois representation of a $p$-adic field a multiset of numbers
called generalized Hodge-Tate weights. In this talk, we regard a $p$-adic local system on a
rigid analytic variety as a geometric family of Galois representations and show that the
multiset of generalized Hodge-Tate weights of the local system is constant.

Communicating Mathematics in Movies: Join award-winning documentary filmmaker Ekaterina Eremenko for a screening of The Discrete Charm of Geometry, followed by a Q&A led by Fields Medalist Efim Zelmanov about Eremenko's work portraying mathematics and mathematicians on film. At the UCSD Price Center Theatre from 5:00-7:00pm on Monday, February 5, 2018.