12:00pm  Zoom  Probability and Analysis Webinar Pavel ZorinKranich  (University of Bonn) TBA 
4:00pm to 5:00pm  Zoom  https://uci.zoom.us/j/97796361534  Applied and Computational Mathematics Axel Almet  (UC Irvine) Inferring the flow of cellcell communication information through singlecell transcriptomics Cellcell communication governs cell fate and decision in health and disease, primarily in the form of biochemical signaling, Understanding what forms of cellcell communication are present and which can be perturbed is crucial to fully understanding the functionality of biological systems. The recent explosion of singlecell RNAsequencing has led to the development of cellcell communication inference methods from gene expression data, enabling new studies on cellcell communication at unprecedented depth and breadth. These methods reveal possible, simultaneous networks of relationships between cell types that are mediated by cell signaling. In this talk, we present ongoing work that extends cellcell communication inference output by inferring possible causal relations between signals. That is, does the presence of one signaling interaction cause a subsequent interaction, leading to a flow of information? We show how cellcell communication and singlecell RNAsequencing data can be framed in the language of causality and thus draw from existing tools developed for causal discovery. We present some preliminary results of our method that have been applied to synthetic data generated by mathematical modeling and suitable singlecell datasets. 
1:00pm to 2:00pm  Zoom  Dynamical Systems Alberto Takase  (UC Irvine) Spectral estimates of dynamicallydefined and amenable operator families Suppose that at each vertex of the Cayley graph of a finitely generated group G is a person holding a dollar. Everybody is told to pass their dollar bill to a neighbor. This can be done so that each person’s net worth increases if and only if the group G is nonamenable. Thus, one can think of nonamenable groups as those where Ponzi schemes can benefit everyone. The Cayley graph of the free group with two generators is an infinite 4valent tree. If everyone passes their dollar towards the origin then everyone’s net worth increases! Because we live in a world where Ponzi schemes don't work, we restrict our attention to amenable groups such as the integer lattice. For dynamicallydefined operator families, the Hausdorff distance of the spectra is estimated by the distance of the underlying dynamical systems while the group is amenable. We prove that if the group has strict polynomial growth and both the group action and the coefficients are Lipschitz continuous, then the spectral estimate has a square root behavior or, equivalently, the spectrum map is $ \frac{1}{2} $Hölder continuous. 
4:00pm to 5:00pm  NS2 1201  Differential Geometry ChaoMing Lin  (UC Irvine) The deformed HermitianYangMills equation and the Csubsolution The deformed HermitianYangMills equation, which will be In this talk, first, I will skim through LeungYauZaslow’s approach in a 
2:00pm to 3:00pm  Rowland Hall 510R  Combinatorics and Probability Paata Ivanishvili  (UCI) Learning low degree functions in logarithmic number of random queries Perhaps a very basic question one asks in learning theory is as follows: we are given a function f on the hypercube {1,1}^n, and we are allowed to query samples (X, f(X)) where X is uniformly distributed on {1,1}^n. After getting these samples (X_1, f(X_1)), ..., (X_N, f(X_N)) we would like to construct a function h which approximates f up to an error epsilon (say in L^2). Of course h is a random function as it involves i.i.d. random variables X_1, ... , X_N in its construction. Therefore, we want to construct such h which can only fail to approximate f with probability at most delta. So given parameters epsilon, delta in (0,1) the goal is to minimize the number of random queries N. I will show that around log(n) random queries are sufficient to learn bounded "lowcomplexity" functions. Based on joint work with Alexandros Eskenazis. 
9:00am to 10:00am  Zoom  Inverse Problems Otmar Scherzer  (University of Vienna & RICAM) Projection and Diffraction Tomography of Particles in a Trap 
11:00am  Zoom ID: 949 5980 546, Password: the last four digits of ID in the reverse order  Harmonic Analysis Jesse GellRedman  (University of Melbourne ) A Fredholm approach to scattering We will give a friendly introduction to the scattering matrix for Schrodinger operators, and discuss how a new functional analytic approach to analysis of nonelliptic equations, due to Vasy, gives a conceptually attractive method for proving detailed regularity results for nonlinear scattering. This is joint work with several groups of authors including Andrew Hassell, Sean Gomes, Jacob Shapiro, and Junyong Zhang. 
3:00pm to 3:50pm  https://uci.zoom.us/j/99192240652  Number Theory Allysa Lumley  (CRM) Primes in short intervals  Heuristics and calculations We formulate, using heuristic reasoning, precise conjectures for the range of the number of primes in intervals of length $y$ around $x$, where $y\ll(\log x)^2$. In particular, we conjecture that the maximum grows surprisingly slowly as $y$ranges from $\log x$ to $(\log x)^2$. We will show that our conjectures are somewhat supported by available data, though not so well that there may not be room for some modification. This is joint work with Andrew Granville.
