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.
CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS SPECIAL SEMINAR: David Carchedi
George Mason University
Dg-manifolds as a model for derived manifolds
on Thursday, April 27, 2017, at 2:00 - 3:00 pm in CMSA Building, 20 Garden St, G10
Given two smooth maps of manifolds ƒ : Μ → L and g : N → L, if they are not transverse, the fibered product M × L N may not exist, or may not have the correct cohomological properties. Thus lack of transverality obstructs many natural constructions in topology and differential geometry. Derived manifolds generalize the concept of smooth manifolds to allow arbitrary (iterative) intersections to exist as smooth objects, regardless of transversality. In this talk we will describe recent progress of ours with D. Roytenberg on giving an accessible geometric model for derived manifolds using differential graded manifolds.

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: Mehran Kardar
MIT
Levitation by Casimir forces in and out of equilibrium
on Thursday, April 27, 2017, at 3:00 pm in CMSA Building, 20 Garden St, G10
Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw's theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint.

THURSDAY SEMINAR : Marc Hoyois
MIT
Bloch-Kato implies Beilinson-Lichtenbaum
on Thursday, April 27, 2017, at 4:00 - 6:00 pm *note change in time this week* in Science Center 507

SPECIAL BASIC NOTIONS SEMINAR: Jean-Pierre Serre
Collège de France
Some simple facts on lattices and orthogonal group representations
on Wednesday, May 03, 2017, at 3:00 pm in Science Center Hall D
Afternoon tea will follow at 4:15 pm in the Math Department Common Room, 4th floor.

JOINT DEPT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: Ilya Soloveychik
Harvard School of Engineering & Applied Sciences
Deterministic Random Matrices
on Wednesday, May 03, 2017, at 3:00 pm in CMSA Building, 20 Garden St, G10
In many applications researchers and engineering need to simulate random symmetric sign (+/-1) matrices (Wigner's matrices). The most natural way to generate an instance of such a matrix is to toss a fair coin, fill the upper triangular part of the matrix with the outcomes and reflect it part into the lower triangular part. For large matrix sizes such approach would require a very powerful source of randomness due to the independence condition. In addition, when the data is generated by a truly random source, atypical non-random looking outcomes have non-zero probability of showing up. Yet another issue is that any experiment involving tossing a coin would be impossible to reproduce exactly, which may be crucial in computer scientific applications. In this talk we focus on the problem of generating n by n symmetric sign matrices based on the similarity of their spectra to Wigner's semicircular law. We develop a simple completely deterministic construction of symmetric sign matrices whose spectra converge to the semicircular law when n grows to infinity. The Kolmogorov complexity of the proposed algorithm is as low as 2 log (n) bits implying that the real amount of randomness conveyed by the semicircular property is quite small.

GAUGE THEORY, TOPOLOGY AND SYMPLECTIC GEOMETRY SEMINAR: Daniel Cristofaro-Gardiner
Harvard University
Two or infinity
on Friday, May 05, 2017, at 3:30 - 4:30 pm in Science Center 507
A central goal in symplectic and contact geometry is to better understand the dynamics of “Reeb” vector fields. About a decade ago, Taubes showed that any Reeb vector field on a closed three-manifold has at least one closed orbit. I will discuss recent joint work showing that, under some hypotheses, any Reeb vector field on a closed three-manifold has either two, or infinitely many, closed orbits. Key tools are an identity relating the lengths of certain sets of Reeb orbits to the volume of the three-manifold, and the theory of global surfaces of section as developed by Hofer, Wysocki, and Zehnder.

SPECIAL LECTURE SERIES: Jean-Pierre Serre
Collège de France
Cohomological invariants mod 2 of Weyl groups, Pt. 1
on Monday, May 08, 2017, at 3:00 - 4:00 PM in Science Center 507
The first lecture will mostly be a résumé of the first part of AMS ULECT 28; the second lecture will give an explicit description of the cohomological invariants of the Weyl groups. *Afternoon tea will follow the talks at 4:15 pm in the Math Department Common Room, 4th Floor.

SPECIAL LECTURE SERIES: Jean-Pierre Serre
Collège de France
Cohomological invariants mod 2 of Weyl groups, Pt. 2
on Tuesday, May 09, 2017, at 3:00 - 4:00 PM in Science Center 507
The first lecture will mostly be a résumé of the first part of AMS ULECT 28; the second lecture will give an explicit description of the cohomological invariants of the Weyl groups. *Afternoon tea will follow the talks at 4:15 pm in the Math Department Common Room, 4th Floor.

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