11:00am to 11:50am - 306 RH - ProbabilityRoman Vershynin - (UCI)Hashing Hashing is a technique widely used in coding theory (an area of computer science) and in cryptography. Although hashing is an interesting mathematical object, it is surprisingly little known to the "mainstream" mathematicians. I will focus on one specific result on hasing, namely the Leftover Hash Lemma. We will state it as a result in extremal combinatorics, give a probabilistic proof of it, and relate it to another fundamental result in extremal combinatorics, the Sauer-Shelah Lemma. |

4:00pm - RH 306 - Differential GeometryMan-Chun Lee - (UBC)Hermitian manifolds with non-positive curvature A recent breakthrough of Wu and Yau asserts that a compact projective Kahler |

12:00pm to 1:00pm - RH 340N - Probability Preprint SeminarMike Cranston - (UCI)Stochastic localization II Stochastic localization is a powerful probabilistic tool invented recently by Ronen Eldan. It has found several applications to challenging problems in probability and geometry, see e.g. https://arxiv.org/abs/1612.01507 |

4:00pm to 5:00pm - RH 306 - ColloquiumLars Hesselholt - (Nagoya University and Copenhagen University)Higher algebra and arithmetic This talk concerns a twenty-thousand-year old mistake: The natural numbers record only the result of counting and not the process of counting. As algebra is rooted in the natural numbers, the higher algebra of Joyal and Lurie is rooted in a more basic notion of number which also records the process of counting. Long advocated by Waldhausen, the arithmetic of these more basic numbers should eliminate denominators. Notable manifestations of this vision include the Bökstedt-Hsiang-Madsen topological cyclic homology, which receives a denominator-free Chern character, and the related Bhatt-Morrow-Scholze integral |

11:00am to 11:50am - PSCB 220 - CryptographyTravis Scholl - (University of California, Irvine)Altug-Chen Candidate Group with Infeasible Inversion A group where finding inverses is hard can be used for many cryptographic constructions. In this talk we will discuss a candidate construction by Salim Ali Altug and Yilei Chen of a group where finding inverses is supposed to be difficult, see https://eprint.iacr.org/2018/926. Their construction works by representing the class group of a quadratic imaginary field as an isogeny graph of an elliptic curve over the ring Z/NZ where N is a product of two primes. After going over the basic constructions, we will discuss some open problems relating to the security of the construction. |

3:00pm to 4:00pm - RH 440R - Nonlinear PDEsChenchen Mu - (UCLA)Mean field games on graphs Mean field game theory is the study of the limit of Nash |

4:00pm - PSCB 140 - Graduate SeminarLi-Sheng Tseng - (UC Irvine)What is cohomology? |