Upcoming Seminars & Events

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March 27, 2017
4:00pm - 5:00pm
Stochastic Models in Robotics and Structural Biology

Many stochastic problems of interest in engineering and science involve random rigid-body motions. In this talk, a variety of stochastic phenomena that evolve on the group of rigid-body motions will be discussed together with tools from harmonic analysis and Lie theory to solve the associated equations. These include mobile robot path planning, statistical mechanics of DNA, and problems in image processing. Current work on multi-robot team diagnosis and repair, information fusion, and self-replicating robots will also be discussed. In order to quantify the robustness of such robots, measures of the degree of environmental uncertainty that they can handle need to be computed. The entropy of the set of all possible arrangements (or configurations) of spare parts in the environment is such a measure, and has led us to study problems at the foundations of statistical mechanics and information theory. These, and other, topics in robotics and structural biology lend themselves to the same mathematical tools, which will be discussed in this talk.

Speaker: Gregory Chikikjian, Johns Hopkins University
Location:
Fine Hall 214
March 27, 2017
5:15pm - 6:15pm
Solving packing problems by linear programming

Part 1:  Optimal configurations of points on manifolds. Classical problems and unexpected solutions.   

The sphere packing problem asks which biggest portion of the euclidean d-dimensional space can be covered by non-overlapping unit balls. In most dimensions d this question is believed be an extremely difficult combinatorial geometric problem. However, in dimensions 8 and 24 the sphere the sphere packing problem has a surprisingly simple solution based on linear programming bounds.The goal of this series of talks is to explain the ideas behind this solution. 

Speaker: Maryna Viazovska , Humboldt University
Location:
Fine Hall 314
March 28, 2017
4:30pm - 5:30pm
Rational curves in projective space with fixed normal bundle

Given a fixed vector bundle E on P^1, one can ask: what is the moduli space of rational curves in P^n with normal bundle E? For projective 3-space, well-known results of Ghione-Sacchiero and Eisenbud-Van de Ven prove that the space of curves with given normal bundle in P^3 is irreducible of the expected dimension, and Eisenbud and Van de Ven conjecture that the same thing holds for arbitrary P^n. Alzati and Re found a single counterexample to this conjecture in P^8. In this talk, I describe joint work with Izzet Coskun finding an infinite family of counterexamples to the conjecture, where we show that the moduli spaces of rational curves with fixed normal bundle can have arbitrarily many components.

Speaker: Eric Riedl , University of Illinois at Chicago
Location:
Fine Hall 322
March 29, 2017
2:30pm - 3:30pm
Applications of Noncommutative Harmonic Analysis in Engineering and the Applied Sciences

This talk will focus more on both the mathematics and the structural biology.

Speaker: Gregory Chirikjian, Johns Hopkins University
Location:
Fine Hall 224
March 29, 2017
3:00pm - 4:00pm
Singular values of random band matrices: Marchenko-Pastur law and more

We consider the limiting spectral distribution of matrices of the form (R+X)(R+X)^∗/(2b_n+1), where X is an n by n band matrix of bandwidth b_n and R is a non random band matrix of bandwidth b_n. We show that the Stieltjes transform of spectrum of such matrices converges to the Stieltjes transform of a non-random measure. And the limiting Stieltjes transform satisfies an integral equation. For R=0, the integral equation yields the Stieltjes transform of the Marchenko-Pastur law. This is a joint work with Indrajit Jana.

Speaker: Alexander Soshnikov , UC Davis
Location:
Fine Hall 214
March 29, 2017
3:00pm - 4:00pm
Embeddedness and convexity for hypersurfaces in hyperbolic space

I will talk a proof of the conjecture of Alexander and Currier on the embeddedness of a nonnegatively curved hypersurfaces in hyperbolic space. I will also discuss some recent works on hypersurfaces with nonnegative Ricci curvature in hyperbolic space.

Speaker: Jie Qing , UC Santa Cruz
Location:
Fine Hall 314
March 29, 2017
4:30pm - 5:30pm
Tableaux combinatorics of hopping particles and Koornwinder polynomials

The asymmetric simple exclusion process (ASEP) is a Markov chain describing particles hopping on a 1-dimensional finite lattice. Particles can enter and exit the lattice at the left and right boundaries, and particles can hop left and right in the lattice, subject to the condition that there is at most one particle per site. The ASEP has been cited as a model for traffic flow, protein synthesis, the nuclear pore complex, etc. In my talk I will discuss joint work with Corteel and with Corteel-Mandelshtam, in which we describe the stationary distribution of the ASEP and the 2-species ASEP using staircase tableaux and rhombic tilings. We also link these models to Askey Wilson polynomials and Macdonald-Koornwinder polynomials, which allows us to give combinatorial formulas for their moments.

Speaker: Lauren Williams , IAS/UCBerkeley
Location:
Fine Hall 314
March 30, 2017
9:30am - 10:30am
The many forms of rigidity for symplectic embeddings

We look at the following chain of symplectic embedding problems in dimension four.

$E(1,a) \to Z^4(A) E(1,a) \to C^4(A) E(1,a) \to P(A,bA) (b \in \mathbb{N}_{\geq 2}) E(1,a) \to T^4(A)$

Here $E(1,a)$ is a symplectic ellipsoid, $Z^4(A)$ is the symplectic cylinder $D^2(A) \times \mathbb{R}^2, C^4(A) = D^2(A) \times D^2(A)$ is the cube and $P(A,bA) = D^2(A) \times D^2(bA)$ the polydisc, and $T^4(A) = T^2(A) \times T^2(A)$, where $T^2(A)$ is the 2-torus of area $A$. In each problem we ask for the smallest $A$ for which $E(1,a)$ symplectically embeds. The answer is very different in each case: total rigidity, total flexibility with a hidden rigidity, and a two-fold subtle transition between them. The talk is based on works by Cristofaro-Gardiner, Frenkel, Latschev, McDuff, Muller, and myself.

Speaker: Felix Schlenk , Universite de Neuchatel, Switzerland
Location:
IAS Room S-101
March 30, 2017
10:45am - 11:45am
TBA - Dusa McDuff
Speaker: Dusa McDuff , Columbia University
Location:
IAS Room S-101
March 30, 2017
2:00pm - 3:30pm
TBA - Ian Jauslin
Speaker: Ian Jauslin , Institute for Advanced Study
Location:
Jadwin Hall 111
March 30, 2017
2:30pm - 3:30pm
TBA - Yongxin Chen

Please note special day (Thursday).

Speaker: Yongxin Chen, Department of Medical Physics, Memorial Sloan Kettering Cancer Center
Location:
McDonnell Hall 102A
March 30, 2017
4:30pm - 5:30pm
Knot traces and concordance

A conjecture of Akbulut and Kirby from 1978 states that the concordance class of a knot is determined by its 0-surgery. In 2015, Yasui disproved this conjecture by providing pairs of knots which have the same 0-surgeries yet which can be distinguished in (smooth) concordance by an invariant associated to the four-dimensional traces of such a surgery. In this talk, I will discuss joint work with Lisa Piccirillo in which we construct many pairs of knots which have diffeomorphic 0-surgery traces yet some of which can be distinguished in smooth concordance by the Heegaard Floer d-invariants of their double branched covers. If time permits, I will also discuss the applicability of this work to the existence of interesting invertible satellite maps on the smooth concordance group.

Speaker: Allison Miller , University of Texas, Austin
Location:
Fine Hall 314
March 30, 2017
4:30pm - 5:30pm
Brief survey of computer assisted proofs for partial differential equations

 I will present a brief survey of computer assisted methods of studying partial differential equations that I have worked on. The methods I am going to discuss allow for obtaining proofs of the existence of particular solutions of a certain class of PDEs in a prescribed range of parameters.  I will discuss opportunities  and limitations of the presented approach. In particular most of the presented results have not been obtained using known techniques of 'classical analysis'.  I will focus on two particular examples from my research, namely 1) a proof of the existence of globally attracting solutions for the 1d viscous Burgers equation (with non-autonomous forcing) https://arxiv.org/abs/1403.7170, and 2) recent proof of the heteroclinic connections in the 1d Ohta-Kawasaki (diblock copolymers) model https://arxiv.org/abs/1703.01022

Speaker: Jacek Cyranka , Rutgers University
Location:
Fine Hall 322
March 30, 2017
4:30pm - 5:30pm
Galois Representations for the general symplectic group

In a recent preprint with Sug Woo Shin (https://arxiv.org/abs/1609.04223) I construct Galois representations corresponding for cohomological cuspidal automorphic representations of general symplectic groups over totally real number fields under the local hypothesis that there is a Steinberg component. In this talk I will explain some parts of this construction that involve the eigenvariety.

Speaker: Arno Kret , University of Amsterdam
Location:
IAS Room S-101
March 31, 2017
9:30am - 5:00pm
Columbia-Princeton Probability Day 2017

Speakers:

  • Marek Biskup (UCLA)
  • Mark Rudelson (Michigan)
  • Vladas Sidoravicius (NYU)
  • Fabio Toninelli (Lyon)

 Junior Speakers:

  • Tatyana Shcherbyna (Princeton)
  • Yi Sun (Columbia)

PLEASE CLICK HERE FOR CONFERENCE LINK.  

Contact Ramon van Handel for further details.

 

Speaker: ,
Location:
TBD
March 31, 2017
5:00pm - 6:00pm
Solving packing problems by linear programming

Part 2: Cohn-Elkies linear programming bounds and modular forms.

The sphere packing problem asks which biggest portion of the euclidean d-dimensional space can be covered by non-overlapping unit balls. In most dimensions d this question is believed be an extremely difficult combinatorial geometric problem. However, in dimensions 8 and 24 the sphere the sphere packing problem has a surprisingly simple solution based on linear programming bounds.The goal of this series of talks is to explain the ideas behind this solution. 

Speaker: Maryna Viazovska , Humboldt University
Location:
Fine Hall 314
April 3, 2017
3:00pm - 4:00pm
TBA - Willie Wong
Speaker: Willie Wong , Michican State University
Location:
Fine Hall 314
April 3, 2017
4:00pm - 5:00pm
TBA - David Steurer
Speaker: David Steurer, Cornell University
Location:
Fine Hall 214
April 3, 2017
5:15pm - 6:15pm
Solving packing problems by linear programming

Part 3: Fourier interpolation.

The sphere packing problem asks which biggest portion of the euclidean d-dimensional space can be covered by non-overlapping unit balls. In most dimensions d this question is believed be an extremely difficult combinatorial geometric problem. However, in dimensions 8 and 24 the sphere the sphere packing problem has a surprisingly simple solution based on linear programming bounds.The goal of this series of talks is to explain the ideas behind this solution. 

Speaker: Maryna Viazovska , Humboldt University
Location:
Fine Hall 314
April 4, 2017
4:30pm - 5:30pm
TBA - Noah Giansiracusa
Speaker: Noah Giansiracusa , Swarthmore College
Location:
Fine Hall 322

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