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 Events
Brian Marcus
UBC
Thu 1 May 2014, 4:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102
Computing entropy and pressure of Z^d Markov Random Fields - Part 2
Math Annex 1102
Thu 1 May 2014, 4:00pm-5:30pm
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UC Berkeley
Mon 12 May 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (PIMS building)
Hölder continuous Euler flows with compact support in space-time [Joint with P. Isett (MIT) ]
ESB 2012 (PIMS building)
Mon 12 May 2014, 3:30pm-4:30pm

Abstract

In this talk, we will describe a construction of compactly supported solutions to the three-dimensional incompressible Euler equations on R \times R^3 with Hölder regularity 1/5 -\epsilon in space and time. This work extends the earlier works of De Lellis-Székelyhidi, Buckmaster-De Lellis-Székelyhidi and Isett on construction of Hölder continuous dissipative Euler flows to the non-periodic setting. Our key technical innovation is a simple method for finding a compactly supported symmetric 2-tensor with a prescribed divergence, which obeys useful bounds.
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Korea Institute for Advanced Study (KIAS)
Tue 13 May 2014, 11:00am
Diff. Geom, Math. Phys., PDE Seminar
ESB 4127
The c-Plateau problem for surfaces in space.
ESB 4127
Tue 13 May 2014, 11:00am-12:00pm

Abstract

The c-Plateau problem for surfaces in space asks, given c>0 and \gamma a closed curve in space, whether we can find M_{c} a smooth orientable surface-with-boundary, with \partial M_{c} = \sigma_{c}+\gamma where \sigma_{c} is a finite union of closed curves disjoint from \gamma, minimizing c-isoperimetric mass \mathbf{M}^{c}(M) := \text{area}(M)+c \cdot \text{length}(\partial M)^{2} amongst all M smooth orientable surfaces-with-boundary, with \partial M = \sigma+\gamma where \sigma is a finite union of closed curves disjoint from \gamma. In this talk we give several regularity results for solutions to the c-Plateau problem, formulated in the more general setting of integer two-rectifiable currents.
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University of Hagen
Tue 13 May 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 4127
Scaling of R\'enyi entanglement entropies of the free Fermi-gas ground state
ESB 4127
Tue 13 May 2014, 3:30pm-4:30pm

Abstract

In the remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Dimitri Gioev and Israel Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bi-partite von-Neumann entanglement entropy of non-interacting fermions in multi-dimensional Euclidean space at zero temperature. Based on recent progress by one of us (A.V.S.) in semi-classical functional calculus for pseudo-differential operators with discontinuous symbols, we provide here a complete proof of that formula and of its generalization to R\'enyi entropies of all orders \alpha>0. The special case \alpha=1/2 is also known under the name logarithmic negativity and often considered to be a particularly useful quantification of entanglement. These formulas, exhibiting a ``logarithmically enhanced area law'', have been used already in many publications.

This is joint work with Hajo Leschke and Alexander V. Sobolev which will be published in Phys. Rev. Lett.
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Université d'Aix-Marseille
Tue 20 May 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Rearrangement inequalities and applications to elliptic eigenvalue problems
ESB 2012
Tue 20 May 2014, 3:30pm-4:30pm

Abstract

The talk will be concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of R^n. To each operator in a given domain, one can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.
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Mon 26 May 2014, 12:00pm SPECIAL
One Time Event
Math 125
Graduation Reception
Math 125
Mon 26 May 2014, 12:00pm-1:30pm

Details

Lunch will be served. There will be award presentations recognizing undergraduate student achievements, followed by the Niven Lecture at 1:30 pm.
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MIT
Mon 26 May 2014, 1:30pm
Department Colloquium
MATH ANNEX 1100
Niven Lecture: Undecidability in number theory
MATH ANNEX 1100
Mon 26 May 2014, 1:30pm-2:30pm

Abstract

Hilbert's Tenth Problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers.  Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists.  But the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be.

Note for Attendees

There will be a departmental reception and student awards from 12:00pm-1:30pm in MATH 125.
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UBC
Tue 27 May 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATX 1118 (Math Annex) NOTE: special location
Monge Ampere functionals and the second boundary value problem
MATX 1118 (Math Annex) NOTE: special location
Tue 27 May 2014, 3:30pm-4:30pm

Abstract

I will discuss a family of fourth order PDE's and their corresponding second boundary value problem on a bounded strictly convex domain. Associated Monge-Amp\`ere functionals will be discussed as well. Special cases here include the equation for prescribed affine mean curvature of a graph, and also Abreu's equation for prescribed scalar curvature of certain toric varieties. The talk is based on joint work with Ben Weinkove.
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