Department of Mathematics FAS Harvard University One Oxford Street Cambridge MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132
To post a seminar which takes place at the Mathematics department, please email seminars@math.harvard.edu with date, time, room, title and possibly with an abstract.
DIFFERENTIAL GEOMETRY SEMINAR: Zhengcheng Gu
PERIMETER INSTITUTE
Topological Quantum Field Theory approach for Bosonic Symmetry-Protected-Topological Phases with Abelian Symmetry in Three Dimensions
on Tuesday, September 01, 2015, at 4:15 PM in Science Center 507
Symmetry protected topological(SPT) phase is a generalization of topological insulator(TI). Different from the intrinsic topological phase, e.g., the fractional quantum hall(FQH) phase, SPT phase is only distinguishable from a trivial disordered phase when certain symmetry is preserved. Indeed, SPT phase has a long history in 1D, and it has been shown that the well known Haldane phase of S=1 Heisenberg chain belongs to this class. However, in higher dimensions, most of the previous studies focus on free electron systems. Until very recently, it was realized that SPT phase also exists in interacting boson/spin systems in higher dimensions. In this talk, I will discuss the general mechanism for bosonic SPT phases and propose a  corresponding topological quantum field theory(TQFT)descriptions. I will focus on examples in three (spacial) dimensions, including bosonic topological insulators(BTI) .

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: Madhu Sudan
Microsoft Research
Robust Low-degree Testing
on Wednesday, September 02, 2015, at 4:00 PM in Science Center 507
Given a function f:F^m to F for a finite field F and integer d, a low-degree tester is a procedure that randomly samples the value of f on a few (potentially correlated) points and makes decision to accept/reject f based on this local view of f. Ideally the tester should accept polynomials of degree at most d with probability 1, and reject functions that are far (in normalized Hamming distance) from every degree d polynomial with probability growing with the distance, and it should do while keeping the local view small. A robust tester is even more ambitious: It would like the local views to be far from acceptable views (again in normalized Hamming distance) if the function being tested is far from acceptable strings. Theoretical computer science has long been interested in the study of low-degree testing --- good tests and analyses have found applications in the fields of probabilistically checkable proofs, locally testable codes, algebraic pseudorandomness, and most recently in the construction of some extremal small set expanders. In the talk I will briefly introduce the problem, mention some of the connections, and explain some basic lower bounds on the size of the local views that a tester can hope to work with. I will summarize some results that show that how testers come close to the lower limits while being robust. Time permitting I will describe a recent approach to robust analysis of low-degree testing via a very general abstract view that only uses the fact that low-degree polynomials are invariant under affine transformations of the domain (F^m), and that they form linear error-correcting codes of good-distance. Based on a long sequence of works, including some recent work with Alan Guo (MIT) and Elad Haramaty (Northeastern).

EVOLUTION EQUATIONS SEMINAR: Long Jin
CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS
Scattering Resonances for Convex Obstacles
on Thursday, September 03, 2015, at 10:00 AM in Science Center 232
In this talk, we discuss the distribution of scattering resonances for strictly convex obstacles in Euclidean spaces and various other background spaces. In particular, we show that under very general boundary conditions, including Dirichlet, Neumann and Robin boundary conditions, there is a cubic resonance free region near the real axis. Moreover, under certain pinched curvature conditions, the resonances appears in cubic bands and the counting functions of the resonances in each band satisfy a Weyl law similar to the one for eigenvalues on compact manifolds.

NUMBER THEORY SEMINAR: Erick Knight
HARVARD UNIVERSITY
A p-adic Jacquet-Langlands Correspondence
on Wednesday, September 09, 2015, at 3:00 - 4:00 PM in Science Center 507
I will construct a p-adic Jacquet-Langlands correspondence, which is a correspondence between Banach space representations of GL_2(Q_p) and Banach space representations of the unit group of the quaternion algebra D over Q_p. The correspondence satisfies local-global compatibility with the completed cohomology of Shimura curves, as well as a compatibility with the classical Langlands correspondence, in the sense that the D* representations can often be shown to have the expected locally algebraic vectors.

MATHEMATICAL PHYSICS SEMINAR : Yu Pin
TSINGHUA UNIVERSITY
Construction of Cauchy data of vacuum Einstein field equations evolving to black holes
on Monday, September 21, 2015, at 12:00 - 2:00 PM in Science Center 232
We show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant time slice in Minkowski space-time inside and exactly a constant time slice in Kerr space-time outside. This is joint with Junbin Li.

MATHEMATICAL PHYSICS SEMINAR : Yu Pin
TSINGHUA UNIVERSITY
Non-existence of multiple-black-hole solutions close to Kerr-Newman
on Monday, October 26, 2015, at 12:00 - 2:00 PM in Science Center 232
We show that a stationary asymptotically flat electro-vacuum solution of Einstein's equations that is everywhere locally "almost isometric" to a Kerr-Newman solution cannot admit more than one event horizon. Axial symmetry is not assumed. This is joint with Willie Wai-Yeung Wong.

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