11:00am to 11:50am  RH 340N  Combinatorics and Probability Elizaveta Rebrova  (UCLA) Modewise JohnsonLindenstrauss embeddings for tensors The celebrated JohnsonLindenstrauss lemma is a powerful tool for dimension reduction via simple (often random) projections that approximately preserve the geometry of the larger dimensional objects. I will discuss an extension of this result to low CPrank tensors. I show how modewise tensor projections preserve tensor geometry in the analogous way, without doing any initial tensor matricization or vectorization. Time permitting, I will also talk about an application to the least squares fitting CP model for tensors. Based on our joint work with Mark Iwen, Deanna Needell, and Ali Zare. 
1:00pm to 2:00pm  RH 440R  Dynamical Systems Denis Gaidashev  ( Uppsala University) Renormalization: from holomorphic dynamics to two dimensions I will describe recent advances in promoting renormalization techniques from one dimensional holomirphic setting to two dimensions, together with the set of questions that these techniques are aiming to address, such as rigidity and geometry of attractors. 
2:00pm to 3:00pm  RH 510R  Working Group in Information Theory Liam Hardiman  (UCI) Conditional Divergence This week, we will continue to discuss Section 2.2 of the lecture notes of Wu and Polyanski: Working Group in Information Theory is a selfeducational project in the department. Techniques based on information theory have become essential in highdimensional probability, theoretical computer science and statistical learning theory. On the other hand, information theory is not taught systematically. The goal of this group is to close this gap. 
1:00pm to 1:50pm  RH 310P  Algebra Sergey Arkhipov  (Aarhus University) Equivariant DGmodules over differential forms and coherent sheaves over derived Hamiltonian reduction This is a joint work in progress with Sebastian Orsted. Given an algebraic variety X acted by an affine algebraic group G, we make sense of the derived category of DGmodules over the DGalgebra of differential forms on X equivariant with respect to differential forms on G. The construction uses an explicit model for a certain homotopy limit of a diagram of DGcategories developed in our earlier work and generalizing a recent result of Block, Holstein and Wei. We compare the obtained category with a certain category of sheaves on the (shifted) cotangent bundle T^*X descending to the Hamiltonian reduction of the cotangent bundle. Two special cases are of interest. In the first, X is a point. Thus we compare comodules over Omega(G) with Gequivariant coherent sheaves on Lie(G). In the second case, X is a simple algebraic group, with the action of the square of the upper triangular subgroup. We obtain a category closely related to the affine Hecke category. 
2:00pm to 3:00pm  RH 340P  Mathematical Physics Wencai Liu  (Texas A&M) The ChristKiselev's multilinear operator technique and its applications to Schrodinger operators We established an axiomatic version of ChristKiselev's multilinear operator techniques. 
3:00pm to 4:00pm  RH 440R  Cryptography Lynn Chua  (UC Berkeley) On the concrete security of the unique Shortest Vector Problem
We study experimentally the Hermite factor of BKZ2.0 on uSVP lattices, with the motivation of understanding the concrete security of LWE in the setting of homomorphic encryption. We run experiments by generating instances of LWE in small dimensions, where we consider secrets sampled from binary, ternary or discrete Gaussian distributions. We convert each LWE instance into a uSVP instance and run the BKZ2.0 algorithm to find an approximation to the shortest vector. When the attack is successful, we can deduce a bound on the Hermite factor achieved for the given blocksize. This allows us to give concrete values for the Hermite factor of the lattice generated for the uSVP instance. We compare the values of the Hermite factors we find for these lattices with estimates from the literature and find that the Hermite factor may be smaller than expected for blocksizes 30, 35, 40, 45. Our work also demonstrates that the experimental and estimated values of the Hermite factor trend differently as we increase the dimension of the lattice, highlighting the importance of a better theoretical understanding of the performance of BKZ2.0 on uSVP lattices. 
3:00pm to 4:00pm  RH 440R  Number Theory Lynn Chua  (UC Berkeley) On the concrete security of the unique Shortest Vector Problem We study experimentally the Hermite factor of BKZ2.0 on uSVP lattices, with the motivation of understanding the concrete security of LWE in the setting of homomorphic encryption. We run experiments by generating instances of LWE in small dimensions, where we consider secrets sampled from binary, ternary or discrete Gaussian distributions. We convert each LWE instance into a uSVP instance and run the BKZ2.0 algorithm to find an approximation to the shortest vector. When the attack is successful, we can deduce a bound on the Hermite factor achieved for the given blocksize. This allows us to give concrete values for the Hermite factor of the lattice generated for the uSVP instance. We compare the values of the Hermite factors we find for these lattices with estimates from the literature and find that the Hermite factor may be smaller than expected for blocksizes 30, 35, 40, 45. Our work also demonstrates that the experimental and estimated values of the Hermite factor trend differently as we increase the dimension of the lattice, highlighting the importance of a better theoretical understanding of the performance of BKZ2.0 on uSVP lattices.

1:00pm to 2:00pm  rh 340p  Mathematical Physics Shiwen Zhang  (U Minnesota) Landscape theory for tightbinding Hamiltonians In 2012, Filoche and Mayboroda introduced the concept of the landscape function u, for an elliptic operator L, which solves the inhomogeneous equation Lu=1. This landscape function has remarkable power to predict the shape and location of localized low energy eigenfunction. These ideas led to beautiful results in mathematics, as well as theoretical and experimental physics. In this talk, we first briefly review these results of landscape theory for differential operators on R^d. We will then discuss some recent progress of extending landscape theory to tightbinding Hamiltonians on discrete lattice Z^d. In particular, we show that the effective potential 1/u creates barrier for appropriate exponential decay eigenfunctions of Agmon type for some discrete Schrodinger operators. We also show that the minimum of 1/u leads to a new counting function, which gives nonasymptotic estimates on the integrated density of states of the Schrodinger operators. This talk contains joint work in progress with S. Mayboroda and some numerical experiments with W. Wang. 