Archive for the ‘Research Lectures’ category

Upcoming Research Lecture: José Seade of UNAM, Cuernavaca to speak on Friday, May 13, 2011

April 28th, 2011

Please join us on Friday, May 13, 2011 as José Seade of UNAM, Cuernavaca will be giving a lecture on Milnor fibrations for real singularities. We will be serving coffee, tea, and cookies starting at 3:30pm and the lecture will begin at 3:45pm.  The lectures will be held in our studio classroom at 929 Massachusetts Avenue Suite #102 in Cambridge. The abstract for Dr. Seade’s talk is listed below and we look forward to seeing you!

Abstract:  In this talk, we will discuss the state of the art concerning Milnor fibrations for real analytic singularities. We will begin by discussing the holomorphic case from a slightly different point of view to the usual one. This throws some new light upon this well-understood setting and lends itself to generalizations to the real setting. Then we discuss the case of real singularities, its similarities and differences with the complex case.

The Worldwide Center of Mathematics (www.centerofmath.org) is located midway between Harvard and Central Squares, at 929 Massachusetts Avenue, Cambridge, MA, in Suite #102. Travel to the Center by public transportation is easy via the #1 bus, or by taking the subway (the T) to Central Square, and walking for 10 minutes. Suite #102 is located on floor 01.

All attendees will need to sign a release form, as the lecture will be recorded for distribution on the Web.

Upcoming Research Lecture: Maria Angelica Cueto to speak on Friday, January 14, 2010

January 13th, 2011

Please join us on Friday, January 14, 2010 as Maria Angelica Cueto of the University of California at Berkeley will be giving a lecture on the implicitization of surfaces via geometric tropicalization. We will be serving coffee, tea, and cookies starting at 3:30pm and the first lecture will begin at 3:45pm.  The lectures will be held in our studio classroom at 929 Massachusetts Avenue Suite #102 in Cambridge. The abstract for Maria Angelica Cueto’s talk is listed below and we look forward to seeing you!

Abstract:  Tropical geometry can be viewed as a polyhedral version of algebraic geometry: algebraic varieties are replaced by weighted balanced polyhedral complexes, in order to answer open questions or to derive simpler proofs of classical results. These objects preserve just enough data about the original varieties to remain meaningful, while discarding much of their complexity.
In this talk we discuss recent developments in tropical methods for implicitization of surfaces. This study was pioneered in the generic case by work of Sturmfels, Tevelev and Yu, and is based on the theory of geometric tropicalization, developed by Hacking, Keel and Tevelev. The latter hinges on computing the tropicalization of subvarieties of tori by analyzing the combinatorics of their boundary in a suitable (tropical) compactification. We enhance this theory by providing a formula for computing weights on tropical varieties, a key tool for tropical implicitization. Finally, we address the question of tropical implicitization for non-generic surfaces and illustrate our techniques with several numerical examples in 3-space.

The Worldwide Center of Mathematics (www.centerofmath.org) is located midway between Harvard and Central Squares, at 929 Massachusetts Avenue, Cambridge, MA, in Suite #102. Travel to the Center by public transportation is easy via the #1 bus, or by taking the subway (the T) to Central Square, and walking for 10 minutes. Suite #102 is located on floor 01.

All attendees will need to sign a release form, as the lecture will be recorded for distribution on the Web.

Upcoming Research Lecture: Hui June Zhu and Thomas Eliot to speak on Friday December 17, 2010

December 16th, 2010

Please join us on Friday, December 17, 2010 as Hui June Zhu of SUNY at Buffalo will be giving a lecture on the construction families of Galois representations. Thomas Eliot will also be giving a short talk on the construction of the convex regular polytopes of every dimension. We will be serving coffee, tea, and cookies starting at 3:30pm and the first lecture will begin at 3:45pm.  The lectures will be held in our studio classroom at 929 Massachusetts Avenue Suite #102 in Cambridge. The abstract for Hui June Zhu’s talk is listed below and we look forward to seeing you!

Abstract: In this talk I will explain how to use Fontaine’s theory of (phi,Gamma)-modules to construct explicit families of n-dimensional crystalline representations, and to compute their mod p reductions. I will also discuss its application in understanding the geometric structure of local Galois deformation space and in proving one direction of a recent modularity conjecture.

The Worldwide Center of Mathematics (www.centerofmath.org) is located midway between Harvard and Central Squares, at 929 Massachusetts Avenue, Cambridge, MA, in Suite #102. Travel to the Center by public transportation is easy via the #1 bus, or by taking the subway (the T) to Central Square, and walking for 10 minutes. Suite #102 is located on floor 01.

All attendees will need to sign a release form, as the lecture will be recorded for distribution on the Web.

Upcoming Research Lecture: Ryan Reich to speak on Friday August 13, 2010

July 27th, 2010

Please join us on Friday, August 13, 2010 as Ryan Reich of Harvard University will be giving a lecture on Beilinson’s “How to glue perverse sheaves.” We will be serving coffee, tea, and cookies starting at 3:30pm and the lecture will begin at 4:00pm.  The lecture will be held in our studio classroom at 929 Massachusetts Avenue Suite #102 in Cambridge. The abstract is listed below and we look forward to seeing you!

Abstract: The titular, foundational work of Beilinson not only gives a technique for gluing perverse sheaves but also implicitly contains constructions of the nearby and vanishing cycles functors of perverse sheaves. These constructions are completely elementary and show that these functors preserve perversity and respect Verdier duality on perverse sheaves. The work also defines a new, “maximal extension” functor, which is left mysterious aside from its role in the gluing theorem. In this talk, we will attempt to clarify some of these notions and results, and present details of some of the constructions and theorems.

The Worldwide Center of Mathematics (www.centerofmath.org) is located midway between Harvard and Central Squares, at 929 Massachusetts Avenue, Cambridge, MA, in Suite #102. Travel to the Center by public transportation is easy via the #1 bus, or by taking the subway (the T) to Central Square, and walking for 10 minutes. Suite #102 is located on floor 01.

All attendees will need to sign a release form, as the lecture will be recorded for distribution on the Web.

Upcoming Research Lecture: Dr. Alexandru Suciu to speak on Friday, July 9, 2010

June 30th, 2010

Please join us on Friday, June 9, 2010 as Dr. Alexandru Suciu of Northeastern University will be giving a lecture about Dwyer-Fried Invariants. We will be serving coffee, tea, and cookies starting at 3:30pm and the lecture will begin at 4:00pm.  The lecture will be held in our studio classroom at 929 Massachusetts Avenue Suite #102 in Cambridge. The abstract is listed below and we look forward to seeing you!

Abstract: Given a finite CW-complex X and a positive integer k, the Galois covers of X with group of deck transformations Z^k are parametrized by the Grassmannian of k-planes in the vector space V = H^1(X, Q). Moving about this rational Grassmannian, and recording when the Betti numbers of the corresponding covers are all finite (up to some fixed degree i) defines certain subsets Omega^i_k(X) of Gr_k(V).

These sets (first studied by Dwyer and Fried in the 1980s) record delicate information on the homological finiteness properties of spaces and groups. I will present a method for determining the sets Omega^i_k(X), using the cohomology jumping loci of X, and the classical incidence correspondence between projective varieties and subvarieties of the Grassmannian. Under favorable conditions, the Omega-invariants are controlled by suitable arrangements of special Schubert varieties. In turn, these arrangements can be computed directly from the cohomology ring of X.


The Worldwide Center of Mathematics, www.centerofmath.org , is located midway between Harvard and Central Squares, at 929 Massachusetts Avenue, Cambridge, MA, in Suite #102. Travel to the Center by public transportation is easy via the #1 bus, or by taking the subway (the T) to Central Square, and walking for 10 minutes. Suite #102 is located on floor 01.

All attendees will need to sign a release form, as the lecture will be recorded for distribution on the Web.