Geometry/Topology Seminar

from Monday
January 01, 2018 to Thursday
May 31, 2018
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Tuesday
February 06, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Jingrui Cheng, University of Wisconsin, Madison
On constant scalar curvature Kaehler metrics

This is a continuation of Chen's colloquium on Feb 1st.


Tuesday
February 13, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Pan Jiayin, Rutgers
Nonnegative Ricci curvature, stability at infinity, and finite generation of fundamental groups

Abstract: In 1968, Milnor conjectured that any open n-manifold $M$ of non-negative Ricci curvature has a finitely generated fundamental group. This conjecture remains open today. In this talk, we show that if there is an integer $k$ such that any tangent cone at infinity of the Riemannian universal cover of $M$ is a metric cone, whose maximal Euclidean factor has dimension $k$, then $π_1(M)$ is finitely generated. In particular, this confirms the Milnor conjecture for a manifold whose universal cover has Euclidean volume growth and unique tangent cone at infinity.


Tuesday
March 06, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Mark Stern, Duke University
Nahm Transform for ALF spaces

I will report on progress (joint with Andres Larrain-Hubach and Sergey Cherkis) on establishing Sergey's conjectured Nahm transform for multicenter Taub NUT spaces.


Tuesday
March 20, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Bianca Santoro, City College
Bifurcation of periodic solutions to the singular Yamabe problem on spheres

In this talk, we describe how to obtain uncountably many periodic solutions to the singular Yamabe problem on a round sphere that blow up along a great circle. These are complete constant scalar curvature metrics on the complement of S^1 inside S^m, m ≥ 5, conformal to the round metric and periodic in the sense of being invariant under a discrete group of
conformal transformations. These solutions come from
bifurcating branches of constant scalar curvature metrics on compact quotients of S^m \ S^1. This is a joint work with R. Bettiol (UPenn) and P. Piccione (USP-Brazil).


Tuesday
April 03, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Lorenzo Foscolo,
TBA

TBA


Tuesday
April 10, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Heather MacBeth, MIT
Kahler-Ricci solitons on resolutions of quotient singularities

By a gluing construction, we produce steady Kahler-Ricci solitons on equivariant crepant resolutions of quotient singularities C^n/G, with the same asymptotics as Cao's soliton on C^n. This is joint work with Olivier Biquard.


Tuesday
April 17, 2018

4:00 PM - 5:30 PM
Math Tower P-131
John Alex Cruz Morales, Universidad Nacional. Colombia, South America
Quantum cohomology of Grassmannians and Lefschetz exceptional collections.

The relations between quantum cohomology and exceptional collections are known since Dubrovin's ICM talk in 1998. Those relations are, in fact, part of the big program of Homological mirror symmetry proposed by Kontsevich in his ICM talk in 1994. In this talk we will discuss some results relating the quantum cohomology of the isotropic Grassmannian IG(2,2n) and its derived category In particular, we will show that certain decomposition of the F-manifold structure of the quantum cohomology is related to certain semiorthogonal decomposition of the derived category. This is a joint work with Alexander Kuznetsov, Anton Mellit, Nicolas Perrin, Maxim Smirnov.


Tuesday
April 24, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Ruobing Zhang, Stony Brook University
Nilpotent Structure and Ricci-Flat Metrics on K3 Surfaces

We will exhibit some new examples of collapsed hyperkähler metrics on a K3 surface which collapse to the standard metric of a closed interval. Geometrically, each regular fiber is a Heisenberg manifold and each singular fiber is a singular circle bundle over a torus. In our example, each bubble limit is either the (multi-)Taub-NUT space or a complete hyperkähler space constructed by Tian-Yau. The regularity estimates in this example in fact confirm a general regularity theory for collapsed Einstein manifolds. We will also discuss some variations of the main gluing construction and some possible developments.


Tuesday
May 01, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Yann Rollin, University of Nantes
Discrete geometry and isotropic surfaces

We consider smooth isotropic immersions from the 2-dimensional torus into R2n, for n≥2. When n=2 the image of such map is an immersed Lagrangian torus of R4. We prove that such isotropic immersions can be approximated by arbitrarily C0-close piecewise linear isotropic maps. If n≥3 the piecewise linear isotropic maps can be chosen so that they are piecewise linear isotropic immersions as well. The proofs are obtained using analogies with an infinite dimensional moment map geometry due to Donaldson. As a byproduct of these considerations, we introduce a numerical flow in finite dimension, whose limit provide, from an experimental perspective, many examples of piecewise linear Lagrangian tori in R4. The DMMF program, which is freely available, is based on the Euler method and shows the evolution equation of discrete surfaces in real time, as a movie.

This is joint work with François Jauberteau and Samuel Tapie.


Show events for:
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