Colloquia/Fall18: Difference between revisions
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Abstract: Mean curvature flow (MCF) of hypersurfaces is the gradient flow of volume functional, which decreases the volume in its steepest way. Any compact MCF will develop singularities in finite time, which are modeled by self-shrinkers, a special class of solutions of MCF. Recently, Colding-Minicozzi proposed a dynamical approach to study the singularities formation of MCF. In this talk, I will survey some progress in the classification of self-shrinkers (from different point views) as well as some major open problems. Part of the work is joint with Jacob Bernstein. | Abstract: Mean curvature flow (MCF) of hypersurfaces is the gradient flow of volume functional, which decreases the volume in its steepest way. Any compact MCF will develop singularities in finite time, which are modeled by self-shrinkers, a special class of solutions of MCF. Recently, Colding-Minicozzi proposed a dynamical approach to study the singularities formation of MCF. In this talk, I will survey some progress in the classification of self-shrinkers (from different point views) as well as some major open problems. Part of the work is joint with Jacob Bernstein. | ||
===October 30: Ruth Charney (Brandeis)=== | |||
Title: Finding hyperbolic behavior in non-hyperbolic spaces | |||
Abstract: In the early 90’s, Gromov introduced a notion of hyperbolicity for geodesic metric spaces. The study of groups of isometries of such spaces has been an underlying theme of much of the work in geometric group theory since that time. Many geodesic metric spaces, while not hyperbolic in the sense of Gromov, nonetheless display some hyperbolic-like behavior. I will discuss a new invariant, the Morse boundary of a space, designed to capture this behavior. This is joint work with Harold Sultan, together with recent work of my students Matt Cordes and Devin Murray. | |||
== Past Colloquia == | == Past Colloquia == | ||
Revision as of 19:21, 23 October 2015
Mathematics Colloquium
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.
Fall 2015
Go to next semester, Spring 2016.
| date | speaker | title | host(s) |
|---|---|---|---|
| September 4 | Isaac Goldbring (UIC) | On Kirchberg's embedding problem | Andrews/Lempp |
| September 11 | Doron Puder (IAS) | Word-Measures on Groups | Gurevich |
| September 18 | Izzet Coskun (UIC) | The geometry of points in the plane | Erman |
| September 25 | Abbas Ourmazd (UW-Milwaukee) | Structure and Dynamics from Random Observations | Mitchell |
| October 2 | |||
| October 9 | Chanwoo Kim | Coercivity of the Boltzmann equation | |
| October 16 | Hadi Salmasian (Ottawa) | The Capelli problem and spectrum of invariant differential operators | Gurevich |
| October 23 | Lu Wang (UW) | Singularities of Mean Curvature Flow | |
| October 30 | Ruth Charney (Brandeis) | Finding hyperbolic behavior in non-hyperbolic spaces | Dymarz |
| November 6 | Chris Rycroft (Harvard) | Spagnolie | |
| November 13 | David Fisher (Indiana) | Dymarz | |
| November 20 | Avy Soffer (Rutgers) | Minh Binh Tran | |
| November 27 | University Holiday | No Colloquium | |
| December 4 | Reserved | ||
| December 11 | Jean-Luc Thiffeault (UW Madison) |
Abstracts
September 4: Isaac Goldbring (UIC)
Title: On Kirchberg's embedding problem
Abstract: In his seminal work on the classification program for nuclear C*-algebras, Kirchberg showed that a particular C*-algebra, the Cuntz algebra O2, plays a seminal role. Subsequent work with Chris Phillips showed that O2 also plays a prominent role in regards to the wider class of exact C*-algebras, and this led Kirchberg to conjecture that every C*-algebra is finitely representable in O2, that is, is embeddable in an ultrapower of O2. The main goal of this talk is to sketch a proof of a local finitary reformulation of this conjecture of Kirchberg. The proof uses model theory and in particular the notion of model-theoretic forcing. No knowledge of C*-algebras or model theory will be assumed. This is joint work with Thomas Sinclair.
September 11: Doron Puder (IAS)
Title: Word-Measures on Groups.
Abstract: Let w be a word in the free group on k generators, and let G be a finite (compact) group. The word w induces a measure on G by substituting the letters of w with k independent uniformly (Haar) chosen random elements of G and evaluating the product. Questions about word-measures on groups attracted attention in recent years both for their own sake and as a tool to analyze random walks on groups.
We will explain some properties of word-measure, give examples and state conjectures. We will also talk about recent results regarding word-measures on symmetric groups and word-measures on unitary groups.
September 18: Izzet Coskun (UIC)
Title: The geometry of points in the plane
Abstract: Grothendieck's Hilbert scheme of points is a smooth compactification of the configuration space of points in the plane. It has close connections with combinatorics, representation theory, mathematical physics and algebraic geometry. In this talk, I will survey some of the basic properties of this beautiful space. If time permits, I will discuss joint work with Arcara, Bertram and Huizenga on codimension one subvarieties of the Hilbert scheme.
September 25: Ourmazd (UW-Milwaukee)
Title: Structure and Dynamics from Random Observations
Abstract: At weddings, the bridal photo is taken under bright lights, with the happy couple holding still. Traditionally in science, the “best” observations are those with the largest signal from the most tightly controlled system. Like bridal photos, the results are not always exciting. In a wide range of phenomena – from the dance of proteins during their function, to the breaking of molecular bonds on the femtosecond scale – tight control is neither possible, nor desirable. Modern data-analytical techniques extract far more information from random sightings than usually obtained from set-piece experiments. I will describe on-going efforts to extract structural and dynamical information from noisy, random snapshots. Examples will include YouTube videos, the structure and conformations of molecular machines such as the ribosome, and the ultrafast dynamics of bond-breaking in small molecules like nitrogen.
October 9: Chanwoo Kim
Title: Coercivity in the Boltzmann equation
Abstract: The Boltzmann equation is a fundamental equation of rarefied gas. Around the natural steady state, so called Maxwellian, a linearized operator is degenerated coercive. In this talk we will see how to recover this degenerated part so that the linearized operator is coercive effectively.
October 16: Hadi Salmasian (Ottawa)
Title: The Capelli problem and spectrum of invariant differential operators
Abstract: The Capelli identity is a mysterious result in classical invariant theory with a long history. It was demystified by Roger Howe, who used it in an ingenious and elegant fashion in the modern theory of representations of real reductive groups. In this talk, I will introduce the Capelli identity, and exhibit the relationship between an extension of this identity with certain polynomials which describe the spectrum of invariant differential operators on symmetric superspaces. These polynomials are analogs of the Jack and Knop-Sahi/Okounkov-Olshanski polynomials. This talk is based on a joint project with Siddhartha Sahi.
October 23: Lu Wang
Title: Singularities of Mean Curvature Flow
Abstract: Mean curvature flow (MCF) of hypersurfaces is the gradient flow of volume functional, which decreases the volume in its steepest way. Any compact MCF will develop singularities in finite time, which are modeled by self-shrinkers, a special class of solutions of MCF. Recently, Colding-Minicozzi proposed a dynamical approach to study the singularities formation of MCF. In this talk, I will survey some progress in the classification of self-shrinkers (from different point views) as well as some major open problems. Part of the work is joint with Jacob Bernstein.
October 30: Ruth Charney (Brandeis)
Title: Finding hyperbolic behavior in non-hyperbolic spaces
Abstract: In the early 90’s, Gromov introduced a notion of hyperbolicity for geodesic metric spaces. The study of groups of isometries of such spaces has been an underlying theme of much of the work in geometric group theory since that time. Many geodesic metric spaces, while not hyperbolic in the sense of Gromov, nonetheless display some hyperbolic-like behavior. I will discuss a new invariant, the Morse boundary of a space, designed to capture this behavior. This is joint work with Harold Sultan, together with recent work of my students Matt Cordes and Devin Murray.