# Upcoming Seminars & Events

## Primary tabs

November 30, 2015
3:15pm - 4:30pm
##### Geometric control: from damped waves to microfluid mixing
###### Analysis Seminar

The damped wave equation is a prototype of a non-selfadjoint PDE, which means that the stationary problem has complex spectrum.  The asymptotic distribution of the spectrum is heavily influenced by properties of the geodesic flow, and in part determines the rate of decay to equilibrium.  In this talk, I will survey recent results on such decay estimates for the damped and over-damped wave equation, followed by a description of work-in-progress applying damped wave methods to systems arriving in the analysis of certain microfluidic mixing devices.

Speaker: Hans Christianson , University of North Carolina
Location:
Fine Hall 110
November 30, 2015
4:30pm - 5:30pm
##### Dissipation at Maximal Rate
###### PACM/Applied Mathematics Colloquium

The lecture will present facets of the conjecture that the role of entropy is to maximize the rate of dissipation.  BIO: Constantine Dafermos was born in Athens, in 1941. He received a diploma in Civil Engineering from the National Technical University, in 1964, and a Ph.D. in Mechanics from Johns Hopkins, in 1967. After teaching for three years at Cornell, he moved to Brown, in 1971, where he is currently a Professor of Applied Mathematics. His work lies at the interface between continuum mechanics and partial differential equations.

Speaker: Constantine M. Dafermos , Brown University
Location:
Fine Hall 214
December 1, 2015
4:30pm - 6:00pm
##### Non-Archimedean geometry in rank >1
###### Algebraic Geometry Seminar

Recent work of Nisse-Sottile, Hrushovski-Loeser, Ducros, and Giansiracusa-Giansiracusa has demonstrated that valuation rings of rank >1 play an important role in the geometry of analytic and tropical varieties over non-Archimedean valued fields of rank 1. In this talk, I will present recent work with Dhruv Ranganathan in which we prove several foundational results on the geometry of analytic and tropical varieties over higher rank valued fields, and recent work with Max Hully in which we use rank 2 valuations to give a new, non-analytic proof of Rabinoff's theorem on the correspondence between tropical and algebraic intersection multiplicities.

Speaker: Tyler Foster , University of Michigan
Location:
Fine Hall 322
December 2, 2015
3:00pm - 4:00pm
##### Random matrices, differential operators and carousels
###### Probability Seminar

The Sine_\beta process is the bulk limit process of the Gaussian beta-ensembles. We show that this process can be obtained as the spectrum of a self-adjoint random differential operator. The result connects the Montgomery-Dyson conjecture about the Sine_2 process and the non-trivial zeros of the Riemann zeta function, the Hilbert-Polya conjecture, and de Brange’s approach of possibly proving the Riemann hypothesis. Our proof relies on the Brownian carousel representation of the Sine_beta process and a connection between hyperbolic carousels and first order differential operators acting on R^2 valued functions. [Joint with B. Virag (Toronto).]

Speaker: Benedek Valko, University of Wisconsin
Location:
Fine Hall 214
December 2, 2015
4:30pm - 5:30pm
##### TBA - Ian Agol
###### Department Colloquium
Speaker: Ian Agol , IAS / Berkeley
Location:
Fine Hall 314
December 3, 2015
2:00pm - 3:30pm
##### TBA - Tatyana Shcherbina
###### Ergodic Theory & Statistical Mechanics
Speaker: Tatyana Shcherbina , IAS
Location:
Fine Hall 601
December 3, 2015
3:00pm - 4:00pm
##### TBA - Steve Ferry
###### Algebraic Topology Seminar
Speaker: Steve Ferry, Rutgers University
Location:
Fine Hall 214
December 3, 2015
3:00pm - 4:00pm
##### TBA - Peter Winkler
###### Discrete Mathematics Seminar
Speaker: Peter Winkler , Dartmouth College
Location:
Fine Hall 224
December 3, 2015
4:30pm - 5:30pm
##### TBA - Haotian Wu
###### Differential Geometry & Geometric Analysis Seminar
Speaker: Haotian Wu, University of Oregon
Location:
Fine Hall 601
December 3, 2015
4:30pm - 5:30pm
##### A tale of two norms
###### Topology Seminar

The first cohomology of a hyperbolic 3-manifold has two natural norms: the Thurston norm, which measure topological complexity of surfaces representing the dual homology class, and the harmonic norm, which is just the L^2 norm on the corresponding space of harmonic 1-forms. Bergeron-Sengun-Venkatesh recently showed that these two norms are closely related, at least when the injectivity radius is bounded below. Their work was motivated by the connection of the harmonic norm to the Ray-Singer analytic torsion and issues of torsion growth in homology of towers of finite covers. After carefully introducing both norms, I will discuss new results that refine and clarify the precise relationship between them; one tool here will be a third norm based on least-area surfaces. This is joint work with Jeff Brock.

Speaker: Nathan Dunfield, University of Illinois
Location:
Fine Hall 314
December 3, 2015
4:30pm - 5:30pm
##### TBA - Anna Mazzucato
###### Analysis of Fluids and Related Topics
Speaker: Anna Mazzucato, Penn State University
Location:
Fine Hall 322
December 3, 2015
4:30pm - 5:30pm
##### Generating series of arithmetic divisors in unitary Shimura varieties
###### Princeton University/IAS Number Theory Seminar

In this talk, I will describe roughly how to define a generating function arithmetic divisors (in Arakelov sense) on a unitary Shimura variety of type (n-1,1). I will then briefly explain why it is modular. If time permits, I will also talk briefly about its application to Gross-Zagier-Zhang type formula and to Colmez conjecture. This is an ongoing joint work with Bruinier, Howard, Kudla and Rapoport.

Speaker: Tonghai Yang , University of Wisconsin
Location:
Fine Hall 214
December 4, 2015
1:30pm - 2:30pm
##### TBA - Lewis Bowen
###### Minerva Distinguished Visitor Lectures
Speaker: Lewis Bowen, University of Texas, Austin & Princeton University
Location:
Fine Hall 110
December 4, 2015
1:45pm - 2:45pm
##### Point-like bounding chains in open Gromov-Witten theory
###### Symplectic Geometry Seminar

Over a decade ago Welschinger defined invariants of real symplectic manifolds of complex dimensions 2 and 3, which count $J$-holomorphic disks with boundary and interior point constraints. Since then, the problem of extending the definition to higher dimensions has attracted much attention. We generalize Welschinger's invariants with boundary and interior constraints to higher odd dimensions using the language of $A_\infty$-algebras and bounding chains. The bounding chains play the role of boundary point constraints. The geometric structure of our invariants is expressed algebraically in a version of the open WDVV equations. These equations give rise to recursive formulae which allow the computation of all invariants for $\mathbb{C}P^n$.  This is joint work with Jake Solomon.

Speaker: Sara Tukachinsky, Hebrew University of Jerusalem
Location:
Fine Hall 322
December 4, 2015
2:45pm - 3:45pm
##### Arithmetic of Double Torus Quotients and the Distribution of Periodic Torus Orbits
###### Ergodic Theory & Statistical Mechanics, Princeton University/IAS Number Theory Seminar

Special Number Theory / Ergodic Theory Seminar -- Note special time and place.

In this talk I will describe some new arithmetic invariants for pairs of torus orbits on inner forms of PGLn and SLn. These invariants allow us to significantly strengthen results towards the equidistribution of packets of periodic torus orbits on higher rank S-arithmetic quotients. An important aspect of our method is that it applies to packets of periodic orbits of maximal tori which are only partially split.

Packets of periodic torus orbits are natural collections of torus orbits coming from a single rational adelic torus and are closely related to class groups of number fields. The distribution of these orbits is akin to the distribution of integral points on homogeneous algebraic varieties with a torus stabilizer.

The distribution of packets of periodic torus orbit has been studied using dynamical methods in the pioneering work of Linnik in the rank 1 case (equidistribution on the 2-sphere) and by Einsiedler, Lindenstrauss, Michel and Venkatesh (ELMV) in higher rank. We note that in rank 1, stronger equidistribution results for packets of periodic orbits have been established by Duke and Iwaniec using the theory of automorphic functions.

The dynamical approach typically consists of two main ingredients: an arithmetic one, which implies that the toral packets have high asymptotic metric entropy, and a measure rigidity argument, which deduces from the entropy result a statement regarding the limit distribution of the orbits. While thanks to Einsiedler, Katok and Lindenstrauss we have very powerful measure rigidity tools for higher rank toral actions, we know much less regarding the arithmetic of these packets in higher rank. A notable exception is the work of ELMV which synergies the dynamical approach with harmonic analysis to prove an equidistribution theorem similar to Linnik’s in the split rank 2 case. In the other cases the current known results, due to the same authors, are significantly weaker.

Our methods generalize Linnik's original arithmetic approach in a different direction. We derive new invariants, akin to the discriminant inner product used by Linnik. These invariants come from studying double quotients of a reductive group by a torus using geometric invariant theory.

We then derive a sharper lower bound for the entropy from these invariants using the action of the Galois group of the torus’ splitting field and the algebraic relations between the invariants. This lower bound gives new qualitative restrictions on the possible limit measures and applies also to partially split maximal tori.

Speaker: Ilya Khayutin, Hebrew University
Location:
Fine Hall 110
December 4, 2015
3:00pm - 4:00pm
##### Tian's properness conjectures, the strong Moser-Trudinger inequality, and infinite-dimensional Finsler geometry
###### Differential Geometry & Geometric Analysis Seminar

In the 90's, Tian introduced a notion of properness in the space of Kahler metrics in terms of Aubin's nonlinear Dirichlet energy and Mabuchi's K-energy and put forward several conjectures on the relation between properness and existence of Kähler-Einstein metrics. These can be viewed as the Kahler analog of the classical Moser-Trudinger inequality from conformal geometry. In joint work with Y. Rubinstein we disprove one of
these conjectures, and prove the remaining ones. Our techniques are flexible and extend to many different situations, including Kahler-Einstein edge metrics and Kahler-Ricci solitons. Moreover, we formulate a
corresponding conjecture for constant scalar curvature metrics and reduce it to a PDE regularity problem of certain weak minimizers of the K-energy.

Speaker: Tamas Darvas , University of Maryland
Location:
Fine Hall 314
December 7, 2015
4:30pm - 5:30pm
##### Faster Convex Optimization - Simulated Annealing with an Efficient Universal Barrier
###### PACM/Applied Mathematics Colloquium

Interior point methods and random walk approaches have been long considered disparate approaches for convex optimization. We show how simulated annealing, one of the most common random walk algorithms, is equivalent, in a certain sense, to the central path interior point algorithm applied to the entropic universal barrier function. Using this observation we improve the state of the art in polynomial time convex optimization in the membership-oracle model.

Speaker: Elad Hazan , Princeton University
Location:
Fine Hall 214
December 8, 2015
4:30pm - 6:00pm
##### Mori fibre spaces for 3-folds in positive characteristic
###### Algebraic Geometry Seminar

There has been much progress in recent years on the LMMP for 3-folds in characteristic p>5. In this talk I will discuss the proof of the base point free theorem and how it leads to termination of the LMMP with scaling and the existence of Mori fibre spaces. This is joint work with Caucher Birkar.

Speaker: Joe Waldron , University of Cambridge
Location:
Fine Hall 322
December 9, 2015
4:30pm - 5:30pm
##### TBA - Peter Selinger
###### Department Colloquium
Speaker: Peter Selinger , Dalhousie University
Location:
Fine Hall 314
December 10, 2015
3:00pm - 4:00pm
##### TBA - Yury Ustinovsky
###### Algebraic Topology Seminar
Speaker: Yury Ustinovsky , Princeton University
Location:
Fine Hall 214