Week of December 1, 2024

Mon Dec 2, 2024
11:00am to 12:00pm - 340P - Machine Learning
Chen Li - (Department of Computer Science, UC Irvine)
Using the Texera System to Teach Data Science and AI/ML Skills Without Coding

Abstract:  

Texera is an open-source system designed to support a cloud-based platform for collaborative data science through GUI-based workflows. Developed over eight years at UCI, it boasts powerful features such as no/low-code requirements, real-time collaboration, shared editing and execution, version control, parallel computing, and debugging. Texera has been effectively used in various educational settings to teach data science and AI/ML skills, particularly to students with little or no programming experience. Notable examples include the Data Science for All summer program (ds4all.ics.uci.edu), which introduces high school students to data science, and UCI’s ICS 80 course (https://canvas.eee.uci.edu/courses/63639/pages/syllabus), aimed at non-STEM undergraduates. In this talk, we will provide an overview of Texera and highlight its unique strengths in teaching data science and AI/ML skills.

4:00pm - RH 340N - Geometry and Topology
Daren Chen - (Caltech)
L-space satellite operators and knot Floer homology

Heegaard Floer homology is a package of invariants for 3 manifolds introduced by Ozsváth and Szabó, which is a symplectic alternative to more gauge theoretic invariants such as monopole Floer homology. A variation of this theory, called knot Floer homology, defines an invariant for knots in 3-manifolds. It was developed independently by Ozsváth and Szabó, and by Rasmussen. In this talk, we will outline the construction, some properties and applications of these invariants. If time permits, I will discuss my recent project to compute the knot Floer homology for a large class of satellite knots. This is joint work with Ian Zemke and Hugo Zhou.

4:00pm to 5:40pm - RH 440 R - Logic Set Theory
Eyal Kaplan - (UC Berkeley)
CANCELLED: Failure of GCH on a measurable with the Ultrapower Axiom

THIS SEMINAR IS UNFORTUNATELY CANCELLED DUE TO CIRCUMSTANCES BEYOND PROFESSOR KAPLAN'S CONTROL.

 

The Ultrapower Axiom (UA) roughly states that any pair of ultrapowers can be compared by internal ultrapowers. The Axiom was extensively studied by Gabriel Goldberg, leading to a series of striking results.

Goldberg asked whether UA is consistent with a measurable cardinal that violates GCH. The main challenge is that UA is not easily preserved under forcing constructions, especially ones that achieve violation of GCH on a measurable from large cardinal assumptions. For example, such forcings might create normal measures which are incomparable in the Mitchell order – a property that negates UA.
In this talk, we sketch the proof that the failure of GCH on the least measurable cardinal can indeed be forced while preserving UA, starting from the minimal canonical inner model carrying a (\kappa, \kappa^{++})-extender. We will present the forcing construction and sketch the main proof ideas. This is a joint work with Omer Ben-Neria.

Tue Dec 3, 2024
3:00pm to 4:00pm - RH 306 - Analysis
Daniel Alpay - (Chapman University)
Infinite dimensional analysis,  models for stochastic processes and new families of stochastic distributions

We briefly review Hida's white noise space theory and some  of its applications to linear stochastic systems and stochastic processes. To define derivatives and stochastic integrals we introduce a family of algebras of stochastic distributions, which are inductive limits of Banach spaces and carry inequalities which are counterparts of the inequality for the norm in a Banach algebra. Non-commutative counterparts and applications to free stochastic processes and their derivatives will be also discussed. 

The talk is based on various collaborations, with in particular Haim Attia, Palle Jorgensen,  Alon Kipnis, David  Levanony, Guy Salomon and Tryphon Georgiou 

4:00pm to 5:00pm - RH306 - Differential Geometry
Eleonora Di Nezza - (Sorbonne Université and Ecole Normale Superieure)
(Weighted) cscK metrics

A central theme in Kähler geometry is the search for canonical Kähler metrics, such as Kähler-Einstein metrics, constant scalar curvature Kähler (cscK for short) metrics, extremal metrics, Kähler-Ricci solutions, etc. The concept of weighted cscK metrics, introduced by Lahdili in 2019, provides a unification of all the above geometric settings. In this talk I will give a panorama of what it is known about these metrics and I will present a criteria for ensuring their existence. This is a joint work with S. Jubert and A. Lahdili.

Wed Dec 4, 2024
3:00pm to 4:00pm - 510R Rowland Hall - Combinatorics and Probability
Anthony Ostuni - (UCSD)
Corners in Quasirandom Groups via Sparse Mixing

We improve the best known upper bounds on the density of corner-free sets over quasirandom groups from inverse poly-logarithmic to quasi-polynomial. We make similarly substantial improvements to the best known lower bounds on the communication complexity of a large class of permutation functions in the 3-player Number-on-Forehead model. Underpinning both results is a general combinatorial theorem that extends the recent work of Kelley, Lovett, and Meka (STOC'24), itself a development of ideas from the breakthrough result of Kelley and Meka on three-term arithmetic progressions (FOCS'23).

Thu Dec 5, 2024
9:00am to 9:50am - Zoom - Inverse Problems
Katie Bouman - (California Institute of Technology)
Seeing Beyond the Blur: Imaging Black Holes with Increasingly Strong Assumptions

https://sites.uci.edu/inverse/

1:00pm - RH 306 - Harmonic Analysis
Grigoris Paouris - (Texas A&M)
A probabilistic approach to the geometry of p-Schatten balls.

On the vector space of matrices equipped with the p-Schatten norm, consider the unit ball normalized to have Lebesque volume 1. Let $ W$ be the random matrix uniformly distributed on this set. We compute sharp upper and lower bounds for the moments of marginals of the random matrix $W$. As an application, we characterize subgaussian and supergaussian directions, estimate the volume of sections of these balls, and provide precise tail estimates for the singular values of the matrix $W$.  Based on a joint work with Kavita Ramanan. 

3:00pm to 4:00pm - Zoom: https://uci.zoom.us/j/91741672832 - Number Theory
Max Weinreich - (Harvard University)
The arithmetic dynamics of the pentagram map

In this talk, we study arithmetic properties of the pentagram map, a dynamical system on convex polygons in the real projective plane. The map sends a polygon to the shape formed by intersecting certain diagonals. This simple operation turns out to define a discrete integrable system, meaning roughly that it can be viewed as a translation map on a family of tori. We show that the pentagram map’s first or second iterate is birational to a translation on a family of Jacobian varieties of algebraic curves. In work in progress, we explore the question of which pentagram-like maps are integrable vs. chaotic. 

Fri Dec 6, 2024
4:00pm to 5:00pm - MSTB 124 - Graduate Seminar
Cynthia Northrup - (Netflix Games)
Alumni Talk Series

Cynthia will walk through her experience after grad school, including advice on finding, applying, and interviewing for jobs. Time will be allotted for questions.