## Seminar Categories

- Applied and Computational Math Colloquium (7)
- Climate Seminar (23)
- Colloquium (4)
- Combinatorics Seminar (1)
- Commutative Algebra Seminar (2)
- Differential Geometry and Symplectic Topology Seminar (4)
- IMA Data Science Lab Seminar (3)
- IMA/MCIM Industrial Problems Seminar (2)
- MCFAM Distinguished Lecture Series (1)
- MCFAM Seminar (2)
- PDE Seminar (1)
- Special Events and Seminars (1)
- Topology Seminar (1)

## Current Series

Fri Sep 13 |
## Probability Seminar2:30pm - Vincent Hall 311Critical behavior for percolation on graphs with given degrees Souvik Dhara, MIT We discuss critical behavior of percolation on finite random networks. In a seminal paper, Aldous (1997) identified the scaling limit for the component sizes in the critical window of phase transition for the Erdos-Renyi random graph (ERRG). Subsequently, there has been a surge in the literature, revealing several interesting scaling limits of these critical components, namely, the component size, diameter, or the component itself when viewed as a metric space. Fascinatingly, when the third moment of the asymptotic degree distribution is finite, many random graph models have been shown to exhibit a universality phenomenon in the sense that their scaling exponents and limit laws are the same as the ERRG. In contrast, when the asymptotic degree distribution is heavy-tailed (having an infinite third moment), the limit law turns out to be fundamentally different from the ERRG case and in particular, becomes sensitive to the precise asymptotics of the highest degree vertices. In this talk, we will focus on random graphs with a prescribed degree sequence. We start by discussing recent scaling limit results, and explore the universality classes that arise from heavy-tailed networks. Of particular interest is a new universality class that arises when the asymptotic degree distribution has an infinite second moment. Not only it gives rise to a completely new universality class, it also exhibits several surprising features that have never been observed in any other universality class so far. This is based on joint works with Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden and Sanchayan Sen. |

Fri Sep 27 |
## Probability Seminar2:30pm - Vincent Hall 311Random matrices, operators and analytic functions Benedek Valko, UW Madison The finite circular beta-ensembles and their point process scaling limit can be represented as the spectra of certain random differential operators. These operators can be realized on a single probability space so that the point process scaling limit is a consequence of an operator level limit. The construction allows the derivation of the scaling limit of the normalized characteristic polynomials of the finite models to a random analytic function. I will review these representations and constructions, and present a couple of applications. Joint with B. Virág (Toronto). |

Fri Oct 04 |
## Probability Seminar2:30pm - Vincent Hall 311Reconstruction problems on amenable graphs Ahmed El Alaoui, Stanford University We consider the problem of reconstructing a hidden assignment of random variables (x_1, , x_n) sitting on the nodes of a graph, given noisy observations of pairs (x_u, x_v) for every edge (u,v) of the graph. Such problems have been extensively studied when the underlying graph is mean-field (e.g., the complete graph, Erdos-Renyi, random regular, ), in which case the existence of a ``possible-but-hard phase where reconstruction is possible but computationally difficult is ubiquitous. In contrast, the picture is dramatically different when the graph is amenable. I will represent a generic result about the optimality of local algorithms for computing marginals under a somewhat strong model of side information. Next, I will focus on Z_2 synchronization (aka planted Ising model) on the Euclidean lattice with weaker side information, and discuss a renormalization-based procedure for reconstructing the assignment. Joint work with Andrea Montanari. |

Fri Oct 04 |
## Probability Seminar3:30pm - Vincent Hall 311Invertibility of inhomogenuous heavy-tailed matrices Galyna Livshyts, Georgia Tech We will show the sharp estimate on the behavior of the smallest singular value of random matrices under very general assumptions. One of the key steps in the proof is a result about the efficient discretization of the unit sphere in an n-dimensional euclidean space. This result allows us to work with very general random matrices. The proof of the result will be outlined. Partially based on the joint work with Tikhomirov and Vershynin. |

Fri Oct 18 |
## Probability Seminar2:30pm - Vincent Hall 311Rare events in the spectrum of random matrices Kevin Leder, UMN In this talk I will consider extreme behavior of the extremal eigenvalues of white Wishart matrices, which play an important role in multivariate analysis. I will focus on the case when the dimension of the feature p is much larger than or comparable to the number of observations n, a common situation in modern data analysis. I will discuss asymptotic approximations for the tail probabilities of the extremal eigenvalues. In addition, I will discuss the construction of an efficient Monte Carlo importance sampling algorithm to estimate the tail probabilities. Simulation results show that our method has the best performance among known approximation approaches, and furthermore provides an efficient and accurate way for evaluating the tail probabilities in practice. Based on joint work with Tiefieng Jiang and Gongjun Xu. |

Fri Oct 25 |
## Probability Seminar2:30pm - Vincent Hall 311Probability Seminar Kevin Leder, UMN |

Fri Nov 08 |
## Probability Seminar2:30pm - Vincent Hall 311"Robust Synchronization via Cycle Consistency Inference Yunpeng Shi, UMN We propose a strategy for improving the existing methods for solving synchronization problems that arise from various computer vision tasks. Specifically, our strategy identifies severely corrupted relative measurements based on cycle consistency information. To the best of our knowledge, this paper provides the first exact recovery guarantees using cycle consistency information. This result holds for a noiseless but corrupted setting as long as the ratio of corrupted cycles per edge is sufficiently small. It further guarantees linear convergence to the desired solution. We also establish stability of the proposed algorithm to sub-Gaussian noise. |

Fri Nov 15 |
## Probability Seminar2:30pm - Vincent Hall 311Joint seminar in math biology and probability: Mathematical Modelling in Immunotherapy of Melanoma Anna Kraut, Bonn Mathematical models can support biomedical research through identification of key mechanisms, validation of experiments, and simulation of new therapeutic approaches. We investigate the evolution of melanomas under adoptive cell transfer therapy with cytotoxic T-cells. It was shown in experiments that phenotypic plasticity, more precisely an inflammation-induced, reversible dedifferentiation, is an important escape mechanism for the tumor. Recently, the effects of possible mutation to a permanently resistant genotype were studied by introducing knockout melanoma cells into the wildtype tumor. We use a stochastic individual-based Markov process to describe the evolution of the tumor under various therapeutic approaches. It is an extension of the model introduced in the paper of Baar et al in 2016 and further includes the effects of T-cell exhaustion and some limited spatial component which results in additional non-linearities. The model is implemented as a hybrid algorithm that combines Gillespie-type stochastic calculations and a deterministic approximation to speed up simulations while keeping the effects of random events. Numerical simulations confirm the resistance to therapy via phenotypic switching as well as genotypic mutation. T-cell exhaustion is identified as an important mechanism that is crucial in fitting the model to the experimental data. We gain further insights into how originally unfit knockout cells can accumulate under therapy, shield the wild type cells from the T-cells, and thus cause an earlier relapse. Going beyond the experiment, the possibility of naturally occurring rare mutations, in contrast to artificially introduced knockout cells, is explored in simulations and produces the same effects. Thus, the clinical relevance of the experimental findings can be confirmed. |

Fri Nov 22 |
## Probability Seminar2:30pm - Vincent Hall 311Spherical spin glass models Eliran Subag, New York University How many critical points does a smooth random function on a high-dimensional space typically have at a given height? how are their distances distributed? what is the volume or geometry of the level sets? can we design efficient optimization algorithms for the random function? For the spherical spin glass models, those questions are closely related to the structure of the Gibbs measures, which have been extensively studied in physics since the 70s. I will start with an overview of the celebrated Parisi formula and ultrametricity property. I will then describe an alternative method to analyze the Gibbs measure using critical points, in the setting of the pure spherical models. Finally, I will explain how the latter can be extended to all spherical models, using another (soft) geometric approach, while at the same time making rigorous and generalizing the famous Thouless-Anderson-Palmer approach from physics. |

Fri Dec 06 |
## Probability Seminar2:30pm - Vincent Hall 311Gibbsian line ensembles and log-gamma polymers Xuan Wu, Columbia University In this talk we will first give an overview of the known |