Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsSpecial Seminar, Aug 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127032&date=2019-08-13
A central question in 3-manifold topology was the Virtual Fibring Conjecture of Thurston, which states that every closed hyperbolic $3$-manifold virtually fibres over the circle. We will discuss Ian Agol's proof of the conjecture, and investigate how one can prove similar statements in the realm of group theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127032&date=2019-08-13Special Seminar, Aug 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127033&date=2019-08-13
We will look into an inductive approach to establishing Kazhdan's property (T) for $SL_n({\mathbb Z})$ and $Aut(F_n)$, and see how one can use computer calculations to cover the base case of the induction.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127033&date=2019-08-13The Cut-Off Phenomenon for the Random-Cluster Model, Aug 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127325&date=2019-08-21
In this presentation, we consider the random-cluster model which is a generalization of the standard edge percolation model. For the random-cluster model on lattice with periodic boundary condition, we prove that the Glauber dynamics exhibits a phenomenon known as the cut-off, especially for the very subcritical regime for all dimensions. This is a joint work with Shirshendu Ganguly.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127325&date=2019-08-21Analysis and PDE Seminar, Aug 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127474&date=2019-08-26
Skyrmions are topologically nontrivial patterns in the magnetization of extremely thin ferromagnets. Typically thought of as stabilized by the so-called Dzyaloshinskii-Moriya interaction (DMI), or antisymmetric exchange interaction, arising in such materials, they are of great interest in the physics community due to possible applications in memory devices.<br />
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In this talk, I will characterize skyrmions as local minimizers of a two-dimensional limit of the full micromagnetic energy, augmented by DMI and retaining the nonlocal character of the stray field energy. In the regime of dominating Dirichlet energy, I will provide rigorous predictions for their size and "wall angles". The main tool is a quantitative stability result for harmonic maps of degree ± 1 from the plane to the two-dimensional sphere, relating the energy excess of any competitor to the homogeneous H¹-distance to the closest harmonic map. This is joint work with Anne Bernand-Mantel and Cyrill B. Muratov.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127474&date=2019-08-26Student Harmonic Analysis and PDE Seminar (HADES), Aug 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127634&date=2019-08-27
Scattering resonances of Schrödinger operator with a compactly supported potential are defined as the poles of the meromorphic continuation of the resolvent. I will introduce the method of complex scaling which produces a natural family of non-self-adjoint operators whose discrete spectrum consists of resonances. Furthermore, we will see that similar results hold in the case of dilation analytic potentials.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127634&date=2019-08-27Topology Seminar (Introductory Talk), Aug 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127439&date=2019-08-28
I will discuss the structure of the ends of tame hyperbolic 3-manifolds and define the end invariants associated to a hyperbolic structure. I will then state Thurston’s Ending Lamination Conjecture, now a theorem of Minsky and Brock-Canary-Minsky. I will model the geometry of a thick degenerate 3-manifold on a certain metric bundle over a Teichmüller geodesic and hint at connections with the complex of curves.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127439&date=2019-08-28Compositions of some random integral mappings (and a conjecture), Aug 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127456&date=2019-08-28
In the 1980's, the Lévy class L of self-decomposable distributions was characterized as distributions of some special random integrals. <br />
That led to more general theory applied to other classes of distributions. Random integral mappings (some type of functionals of Lévy processes) are continuous homomorphisms between <br />
convolution sub-semigroups of ID (the semigroup of all infinitely divisible measures). We will show that compositions of those random integrals (mappings) can be always expressed as <br />
another single random integral mapping. That fact is illustrated by some old (Thorin class T) and new examples of distributions (free infinite divisibility).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127456&date=2019-08-28Topology Seminar, Aug 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127440&date=2019-08-28
In this talk, I will define bounded cohomology of groups with an emphasis on examples coming from computing the volumes of locally geodesic simplices in hyperbolic manifolds. We will see that the volume class associated to a hyperbolic structure identifies its geometrically infinite end invariants or those of the covering spaces associated to virtual fibers. We will also study the behavior of linear combinations of volume classes, and give a geometric interpretation of addition in some special cases.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=127440&date=2019-08-28