Upcoming Seminars & Events

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November 27, 2017
3:00pm - 4:00pm
Stochastic homogenization: renormalization, regularity, and quantitative estimates

There has been a lot of work in recent years on the problem of understanding the behavior of solutions of PDEs with random coefficients, with most of the work focused on linear elliptic equations in divergence form. I will give an overview of recent joint works with Smart, Kuusi and Mourrat in which we introduce a ``renormalization group" method, which leads to a very precise, quantitative description of the solutions.

Speaker: Scott Armstrong, Courant Institute of Mathematical Sciences, New York University
Location:
Fine Hall 314
November 27, 2017
4:00pm - 5:00pm
TBA-Yu-Shen Lin
Speaker: Yu-Shen Lin, CMSA, Harvard University
Location:
IAS Room S-101
November 27, 2017
4:00pm - 5:00pm
Two problems involving breakup of a liquid film

Understanding the breakup of a liquid film is complicated by the fact that there is no obvious instability driving breakup: surface tension favors a film of uniform thickness over a deformed one. Here, we identify two mechanisms driving a film toward (infinite time) pinch-off. In the first problem, we show how the rise of a bubble is arrested in a narrow tube, on account of the lubricating film pinching off. In the second problem, breakup of a free liquid film is driven by a strong temperature gradient across the pinch region. 

Speaker: Jens Eggers, Bristol University
Location:
Fine Hall 214
November 28, 2017
4:30pm - 5:30pm
The Hilbert scheme of points on singular surfaces.

The Hilbert scheme of points on a quasi-projective variety parametrizes its zero-dimensional subschemes. When the variety is a singular surface, the geometry of the Hilbert scheme reflects the singularity of the underlying surface. I will present some work in progress on the Hilbert schemes of points on surfaces of embedding dimension three and four. Part of the talk will be on a joint work with Lawrence Ein.

Speaker: Xudong Zheng , Johns Hopkins
Location:
Fine Hall 322
November 28, 2017
4:30pm - 5:30pm
TBA - Dr. Efi Efrati
Speaker: Dr. Efi Efrati, Weizmann Institute
Location:
Jadwin Hall 343
November 28, 2017
4:45pm - 5:45pm
Shimura curves and new abc bounds

Existing unconditional progress on the abc conjecture and Szpiro's conjecture is rather limited and coming from essentially only two approaches: The theory of linear forms in p-adic logarithms, and bounds for the degree of modular parametrizations of elliptic curves by using congruences of modular forms. In this talk I will discuss a new approach as well as some unconditional results that it yields.

Speaker: Hector Pasten, Harvard University
Location:
IAS Room S-101
November 29, 2017
2:30pm - 3:30pm
Data-driven analysis of neuronal activity

Recent advances in experimental methods in neuroscience enable the acquisition of large-scale, high-dimensional and high-resolution datasets. These complex and rich datasets call for the development of advanced data analysis tools, as commonly used techniques do not suffice to capture the spatiotemporal network complexity. In this talk I will present new data-driven methods based on global and local spectral embeddings for the processing and organization of high-dimensional datasets, and demonstrate their application to the analysis of neuronal measurements.  

Speaker: Gal Mishne, Yale University
Location:
Fine Hall 224
November 29, 2017
3:00pm - 4:00pm
TBA-Timo Seppalainen
Speaker: Timo Seppalainen, University of Wisconsin
Location:
Fine Hall 214
November 29, 2017
4:30pm - 5:30pm
Regularity of area-minimizing surfaces in higher codimension: old and new

The theory of integral currents, developed by Federer and Fleming in the 60s, gives a powerful framework to solve the Plateau's problem in every dimension and codimension. The interior and boundary regularity theory for the codimension

one case is  rather well understood, thanks to the work of several mathematicians in the 60es, 70es and 80es.

 

Speaker: Camillo De Lellis, Institut fuer Mathematik Universitaet Zuerich
Location:
Fine Hall 314
November 30, 2017
12:30pm - 1:30pm
TBA-Amina Abdurrahman
Speaker: Amina Abdurrahman, Princeton University
Location:
Fine Hall 110
November 30, 2017
1:30pm - 3:30pm
TBA-Joel Moreira
Speaker: Joel Moreira, Northwestern University
Location:
Fine Hall 1001
November 30, 2017
3:00pm - 4:00pm
Multiplicative structure of the cohomology of real toric spaces

A real toric space is a topological space which admits a well-behaved \Z_2^k-action.

Real moment-angle complexes, real toric varieties and small covers are typical examples of real toric spaces.

A real toric space is determined by the pair of a simplicial complex K and a characteristic matrix \Lambda.

    

In this talk, we discuss an explicit -cohomology ring formula of a real toric space in terms of K and \Lambda, where R is a commutative ring with unity in which 2 is a unit. Interestingly, it has a natural (\Z \oplus \row \Lambda)-grading.

 

Speaker: Suyoung Choi, Ajou University/Northeastern University
Location:
Fine Hall 110
November 30, 2017
4:30pm - 5:30pm
Singularity formation in the contour dynamics for 2d Euler equation on the plane.

We will study 2d Euler dynamics of centrally symmetric pair of patches on the plane. In the presence of exterior regular velocity, we will show that these patches can merge so fast that the distance between them allows double-exponential upper bound which is known to be sharp. The formation of the 90 degree corners on the interface and the self-similarity analysis of this process will be discussed. For a model equation, we will prove existence of the curve of smooth stationary solutions that originates at singular stationary steady state.

Speaker: Serguei Denissov, University of Wisconsin
Location:
Fine Hall 322
November 30, 2017
4:30pm - 5:30pm
Locally symmetric spaces: p-adic aspects

p-adic period spaces have been introduced by Rapoport and Zink as a generaliza- tion of Drinfeld upper half spaces and Lubin-Tate spaces. Those are open subsets of a rigid analytic p-adic flag manifold. An approximation of this open subset is the so called weakly admissible locus obtained by removing a profinite set of closed Schubert varieties. I will explain a recent theorem characterizing when the period space coincides with the weakly admissible locus. The proof consists in a thorough study of modifications of G-bundles on the curve.

Speaker: Laurent Fargues, CNRS/IMJ Paris
Location:
IAS Room S-101
November 30, 2017
4:30pm - 5:30pm
Irreducible SL(2,C)-representations of integer homology 3-spheres

We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. This uses instanton gauge theory, and in particular a non-vanishing result of Kronheimer-Mrowka and some new results that we establish for holonomy perturbations of the ASD equation.

Speaker: Raphael Zentner, University of Regensburg (Germany)
Location:
Fine Hall 314
December 4, 2017
3:00pm - 4:00pm
TBA-Maria Colombo
Speaker: Maria Colombo, ETH Zürich
Location:
Fine Hall 314
December 5, 2017
3:00pm - 4:30pm
Attractors: "when inertial waves meet topography..."
Speaker: Laure Saint-Raymond, Minerva Distinguished Visitor, Princeton University and Professor, École Normale Supérieure de Lyon
Location:
Fine Hall 1201
December 5, 2017
4:30pm - 5:30pm
Bulk-Edge Duality and Complete Localization for Chiral Chains

We study one dimensional insulators obeying a chiral symmetry in the single-particle picture where the Fermi energy is assumed to lie within a mobility gap. Topological invariants are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given bulk system with nearest neighbor hopping, the invariant is equal to the induced-edge-system's invariant.

Speaker: Jacob Shapiro, ETH
Location:
Jadwin Hall 343
December 5, 2017
4:30pm - 5:30pm
Foliated surfaces and their stable reduction.

In 1977 Bogomolov proved that on surfaces of general type with c_1^2>c_2, curves of a given genus form a bounded family. The role played by foliations in his proof was further investigated by McQuillan, who in 1998 proved the Green-Griffiths conjecture for surfaces of general type with c_1^2>2c_2.

Speaker: Federico Buonerba, New York University
Location:
Fine Hall 322
December 5, 2017
4:45pm - 5:45pm
TBA-Jun Su
Speaker: Jun Su, Princeton University
Location:
IAS Room S-101

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