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4:00pm to 5:00pm - RH 306 - Applied and Computational Mathematics Solmaz Kia - (Mechanical and Aerospace Eng. Dept., University of California Irvine) Control theoretic approaches to distributed in-network convex optimization In recent years, there has been a renewed research interest in finding efficient algorithms for solving convex optimization problems in a parallel or distributed fashion. This trend has been mainly motivated by the explosion in size and complexity of data-sets used in statistical machine learning and applications in modern cyberphysical systems, communication networks, and other applications in networked systems. This talk presents how automatic control-theoretic tools contribute to developing and analyzing distributed convex optimization algorithms systematically. Bio: Solmaz S. Kia who an associate professor of Mechanical and Aerospace Engineering at the University of California Irvine (UCI), with a joint appointment at the Computer Science department. She obtained her Ph.D. degree in Mechanical and Aerospace Engineering from UCI, in 2009, and her M.Sc. and B.Sc. in Aerospace Engineering from the Sharif University of Technology, Iran, in 2004 and 2001, respectively. She was a senior research engineer at SySense Inc., El Segundo, CA from Jun. 2009-Sep. 2010. She held postdoctoral positions in the Department of Mechanical and Aerospace Engineering at UC San Diego and UCI. She was the recipient of the prestigious UC President's Postdoctoral Fellowship from 2012-2014. She is also a recipient of the 2017 NSF CAREER award and the 2021 IEEE Control Systems best paper award. Dr. Kia is a senior member of IEEE and serves as an associate editor for Automatica, IEEE Transactions on Control of Network Systems, IEEE Open Journal of Control Systems and IEEE Sensors Letters. Dr. Kia's main research interests, in a broad sense, include nonlinear control theory, distributed optimization/coordination/estimation, and probabilistic robotics. |
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4:00pm - ISEB 1200 - Differential Geometry Pak-Yeung Chan - (UC San Diego) Hamilton-Ivey estimates for gradient Ricci solitons One special feature for the Ricci flow in dimension 3 is the |
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2:00pm to 3:00pm - 510R Rowland Hall - Combinatorics and Probability Roman Vershynin - (UCI) Mathematics of synthetic data. II. Random walks. In this talk we will reduce the problem of constructing private synthetic data to a construction of a superregular random walk. Such walk locally looks like a simple random walk, but which globally deviates from the origin much slower than the Brownian motion. Joint work with March Boedihardjo and Thomas Strohmer, https://arxiv.org/abs/2204.09167 |
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9:00am to 10:00am - Zoom - Inverse Problems Gregory Eskin - (UCLA) Rigidity for Lorentzian metrics having the same length of null-geodesics |
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10:00am to 11:00am - https://uci.zoom.us/j/95268809663 - Number Theory Amita Malik - (Max Planck Institute) Partitions into primes with a Chebotarev condition In this talk, we discuss the asymptotic behavior of the number of integer partitions into primes concerning a Chebotarev condition. In special cases, this reduces to the study of partitions into primes in arithmetic progressions. While the study for ordinary partitions goes back to Hardy and Ramanujan, partitions into primes have been re-visited recently. Our error term is sharp and in the particular case of partitions into prime numbers, we improve on a result of Vaughan. In connection with the monotonicity result of Bateman and Erd\H{o}s, we give an asymptotic formula for the difference of the number of partitions of positive integers which are k-apart. |
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11:00am - RH 306 - Harmonic Analysis Yizhe Zhu - (UCI) The characteristic polynomial of sums of random permutations Let $A_n$ be the sum of $d$ permutations matrices of size $n×n$, each drawn uniformly at random and independently. We prove that $\det( I_n−zA_n/\sqrt{d})$ converges when $n\to\infty$ towards a random analytic function on the unit disk. As an application, we obtain an elementary proof of the spectral gap of random regular digraphs with a sharp constant. Our results are valid both in the regime where $d$ is fixed and for $d$ slowly growing with $n$. Joint work with Simon Coste and Gaultier Lambert. |
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1:00pm - Rowland 510R - Algebra Cris Negron - (University of Southern California) Vanishing tests for (quantum) group representations In this talk I will survey some results on the vanishing of (quantum) group representations, at the level of the stable category. Equivalently, I will discuss effective ways to test projectivity of a given finite-dimensional G-representation, where G your favorite finite (quantum) group. In the case of an elementary abelian p-group E, over k=\bar{F}_p, for example, Carlson tells us that an object V in rep(E) is projective if and only if V has projective restriction along each flat algebra map \alpha: k[t]/(t^p) -> k[E] into the group ring. One thus reduces a wild representation type calculation to a finite representation type calculation, via this P^{rank(E)}(k)-family of embeddings. I will provide an analogous vanishing result for the small quantum group u_q(L), which involves the introduction of a G/B-family of small quantum Borels and an analysis of certain ``noncommutative complete intersections”. This is joint work with Julia Pevtsova [arxiv:2012.15453, arxiv:2203.10764]. |
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2:00pm to 3:00pm - 306 - Mathematical Physics Jiranan Kerdboon - (U Mississippi) Anderson Localization for Schrödinger Operators with Monotone Potentials over Circle Diffeomorphisms We generalize localization results on 1D quasiperiodic Schrödinger operators with monotone potentials over Diophantine irrational rotations to the results over circle diffeomorphisms with irrational rotation numbers. Our results show that the class of irrational rotation numbers can be extended to weakly Liouville irrationals |
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4:00pm to 5:00pm - MSTB 124 - Graduate Seminar Connor Mooney - (UC Irvine) Optimal transport and the Monge-Ampere equation The optimal transport problem asks: What is the cheapest way to transport goods (e.g. bread in bakeries) to desired locations (e.g. grocery stores)? Although simple to state, this problem is tricky to solve. Optimal transport is closely related to a nonlinear PDE called the Monge-Ampere equation, and important questions about optimal transport can be approached using this connection. In this talk we will discuss optimal transport, its connection to the Monge-Ampere equation, and some recent applications of optimal transport theory in geometric and functional inequalities and meteorology. |