Photos of the event can be found on CMSA’s Blog.
Organizers:
* This event is sponsored by CMSA Harvard University.
Monday, March 27
Time  Speaker  Title 
8:30am – 9:00am  Breakfast  
9:00am – 10:00am  Kieron Burke, University of California, Irvine  Background in DFT and electronic structure calculations 
10:00am – 11:00am  Kieron Burke, University of California, Irvine 
The density functionals machines can learn 
11:00am – 12:00pm  Sadasivan Shankar, Harvard University  A few key principles for applying Machine Learning to Materials (or Complex Systems) — Scientific and Engineering Perspectives 
Tuesday, March 28
Time  Speaker  Title 
8:30am – 9:00am  Breakfast  
9:00am – 10:00am  Ryan Adams, Harvard  TBA 
10:00am – 11:00am  Gábor Csányi, University of Cambridge 
Interatomic potentials using machine learning: accuracy, transferability and chemical diversity 
11:00am – 1:00pm  Lunch Break  
1:00pm – 2:00pm  Evan Reed, Stanford University  TBA 
Wednesday, March 29
Time  Speaker  Title 
8:30am – 9:00am  Breakfast  
9:00am – 10:00am  Patrick Riley, Google  The Message Passing Neural Network framework and its application to molecular property prediction 
10:00am – 11:00am  Jörg Behler, University of Göttingen  TBA 
11:00am – 12:00pm  Ekin Doğuş Çubuk, Stanford Univers  TBA 
4:00pm  Leslie Greengard, Courant Institute  Inverse problems in acoustic scattering and cryoelectron microscopy
CMSA Colloquium 
Thursday, March 30
Time  Speaker  Title 
8:30am – 9:00am  Breakfast  
9:00am – 10:00am  Matthias Rupp, Fitz Haber Institute of the Max Planck Society  TBA 
10:00am – 11:00am  Petros Koumoutsakos, Radcliffe Institute for Advanced Study, Harvard  TBA 
11:00am – 1:00pm  Lunch Break  
1:00pm – 2:00pm  Dennis Sheberla, Harvard University  Rapid discovery of functional molecules by a highthroughput virtual screening 
Registration and additional information on the conference can be found at http://abel.harvard.edu/jdg/index.html.
Confirmed Speakers
* This event is cosponsored by Lehigh University and partially supported by the National Science Foundation.
]]>This event is open and free. If you would like to attend, please register here to help us keep a headcount. A list of lodging options convenient to the Center can also be found on our recommended lodgings page.
Speakers:
Orr Ashenberg, Fred Hutchinson Cancer Research Center
John Barton, Massachusetts Institute of Technology
Simona Cocco, Laboratoire de Physique Statistique de l’ENS
Sean Eddy, Harvard University
Efthimios Kaxiras, Harvard University
Michael Laub, Massachusetts Institute of Technology
Debora S. Marks, Harvard University
Govind Menon, Brown University
Rémi Monasson, Laboratoire de Physique Théorique de l’ENS
Andrew Murray, Harvard University
Ilya Nemenman, Emory College
Chris Sander, DanaFarber Cancer Institute, Harvard Medical School
Dave Thirumalai, University of Texas at Austin
Martin Weigt, IBPS, Université Pierre et Marie Curie
Matthieu Wyart, EPFL
More speakers will be confirmed soon.
May 1, Monday
Time  Speaker  Topic 
9:0010:00am  Sean Eddy  TBA 
10:0011:00am  Mike Laub  TBA 
11:00am12:00pm  Ilya Nemenman  TBA 
Time  Speaker  Topic 
9:0010:00am  Orr Ashenberg  TBA 
10:0011:00am  Debora Marks  TBA 
11:00am12:00pm  Martin Weigt  TBA 
4:30pm5:30pm  Simona Cocco  CMSA Colloquia 
Time  Speaker  Topic 
9:0010:00am  Andrew Murray  TBA 
10:0011:00am  Matthieu Wyart  TBA 
11:00am12:00pm  Rémi Monasson  TBA 
Time  Speaker  Topic 
9:0010:00am  David Thirumalai  TBA 
10:0011:00am  Chris Sander  TBA 
11:00am12:00pm  John Barton  TBA 
Organizers:
Michael Brenner, Lucy Colwell, Elena Rivas, Eugene Shakhnovich
* This event is sponsored by CMSA Harvard University.
Confirmed speakers:
The conference is coorganized by Denis Auroux and Victor Guillemin. Additional information on the conference will be announced closer to the event.
Time  Speaker  Topic 
8:30am – 9:0am  Breakfast  
9:00am – 10:00am  Jonathan Weitsman  Title: On the geometric quantization of (some) Poisson manifolds 
10:30am – 11:30am  Eckhard Meinrenken  Title: On Hamiltonian loop group spaces
Abstract: Let G be a compact Lie group. We explain a construction of an LGequivariant spinor module over any Hamiltonian loop group space with proper moment map. It may be regarded as its `canonical spinc structure’. We show how to reduce to finite dimensions, resulting in actual spins structure on transversals, as well as twisted spinc structures for the associated quasihamiltonian space. This is based on joint work with Yiannis Loizides and Yanli Song. 
11:30am – 1:30pm  Break  
1:30pm – 2:30pm  Ana Rita Pires  Title: Infinite staircases in symplectic embedding problems
Abstract: McDuff and Schlenk studied an embedding capacity function, which describes when a 4dimensional ellipsoid can symplectically embed into a 4ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with CristofaroGardiner, Holm and Mandini. 
3:00pm – 4:00pm  Sobhan Seyfaddini  Title: Rigidity of conjugacy classes in groups of areapreserving homeomorphisms
Abstract: Motivated by understanding the algebraic structure of groups of areapreserving homeomorphims F. Beguin, S. Crvoisier, and F. Le Roux were lead to the following question: Can the conjugacy class of a Hamiltonian homeomorphism be dense? We will show that one can rule out existence of dense conjugacy classes by simply counting fixed points. This is joint work with Le Roux and Viterbo. 
4:30pm – 5:30pm  Roger Casals  Title: Differential Algebra of Cubic Graphs Abstract: In this talk we will associate a combinatorial dgalgebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations and examples. From there we study the Legendrian surfaces behind these constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.Video 
June 6, Tuesday (Full day)
Time  Speaker  Topic 
8:30am – 9:00am  Breakfast  
9:00am – 10:00am  Alejandro Uribe  Title: Semiclassical wave functions associated with isotropic submanifolds of phase space
Abstract: After reviewing fundamental ideas on the quantumclassical correspondence, I will describe how to associate spaces of semiclassical wave functions to isotropic submanifolds of phase space satisfying a BohrSommerfeld condition. Such functions have symbols that are symplectic spinors, and they satisfy a symbol calculus under the action of quantum observables. This is the semiclassical version of the Hermite distributions of Boutet the Monvel and Guillemin, and it is joint work with Victor Guillemin and Zuoqin Wang. I will inlcude applications and open questions. 
10:30am – 11:30am  Alisa Keating  Title: Symplectomorphisms of exotic discs
Abstract: It is a theorem of Gromov that the group of compactly supported symplectomorphisms of R^4, equipped with the standard symplectic form, is contractible. While nothing is known in higher dimensions for the standard symplectic form, we show that for some exotic symplectic forms on R^{4n}, for all but finitely n, there exist compactly supported symplectomorphisms that are smoothly nontrivial. The principal ingredients are constructions of Milnor and Munkres, a symplectic and contact version of the Gromoll filtration, and Borman, Eliashberg and Murphy’s work on existence of overtwisted contact structures. Joint work with Roger Casals and Ivan Smith. 
11:30am – 1:30pm  Break  
1:30pm – 2:30pm  Chen He  Title: Morse theory on bsymplectic manifolds
Abstract: bsymplectic (or logsymplectic) manifolds are Poisson manifolds equipped with symplectic forms of logarithmic singularity. Following Guillemin, Miranda, Pires and Scott’s introduction of Hamiltonian group actions on bsymplectic manifolds, we will survey those classical results of Hamiltonian geometry to the bsymplectic case. 
3:00pm – 4:00pm  Yael Karshon  Title: Geometric quantization with metaplecticc structures
Abstract: I will present a variant of the KostantSouriau geometric quantization procedure that uses metaplecticc structures to incorporate the “half form correction” into the prequantization stage. This goes back to the late 1970s but it is not widely known and it has the potential to generalize and improve upon recent works on geometric quantization. 
The topic of the talks are as follows:
Date  Title  Abstract 
332017  Modularity of DT invariants on smooth K3 fibrations I  Motivated by Sduality modularity conjectures in string theory, we study the DonaldsonThomas invariants of 2dimensional sheaves inside a nonsingular threefold X. Our main case of study is when X is given by a smooth surface fibration over a curve with the canonical bundle of X pulled back from the base curve. We study the DonaldsonThomas invariants, as defined by Richard Thomas, of the 2dimensional Gieseker stable sheaves in X supported on the fibers. In case whereXis aK3 fibration, analogous to the GromovWitten theory formula established by MaulikPandharipande, we express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the fiber and the NoetherLefschetz numbers of the fibration, and prove that the invariants have modular properties. We are intending to go through these lectures with a relatively slow speed, that is: TheoremProof style, (so we will be less handwavy!) and we intend to establish some of the required background, e.g NoetherLefschetz theory, vector valuedmodular forms etc. 
382017  Modularity of DT invariants on smooth K3 fibrations II  Motivated by Sduality modularity conjectures in string theory, we study the DonaldsonThomas invariants of 2dimensional sheaves inside a nonsingular threefold X. Our main case of study is when X is given by a smooth surface fibration over a curve with the canonical bundle of X pulled back from the base curve. We study the DonaldsonThomas invariants, as defined by Richard Thomas, of the 2dimensional Gieseker stable sheaves in X supported on the fibers. In case whereXis aK3 fibration, analogous to the GromovWitten theory formula established by MaulikPandharipande, we express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the fiber and the NoetherLefschetz numbers of the fibration, and prove that the invariants have modular properties. We are intending to go through these lectures with a relatively slow speed, that is: TheoremProof style, (so we will be less handwavy!) and we intend to establish some of the required background, e.g NoetherLefschetz theory, vector valued modular forms etc. 
3102017  Conifold Transitions and modularity of DT invariants on Nodal fibrations 
Following lectures I and II we continue the discussion on the moduli space of shaves with two dimensional support on K3fibered threefolds, which can admit finitely many nodal (rational double point singularity at worst) fibers. We will use the conifold transitions and degeneration techniques in this case to relate the geometry of our moduli space and its enumerative invariants to the ones studied in lectures I, II over smooth K3fibrations.

452017  Stable pair PT invariants on smooth fibrations I  We study PandharipandeThomas’s stable pair theory on smooth K3 fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of KawaiYoshioka’s formula for the Euler characteristics of moduli spaces of stable pairs on K3 surfaces and NoetherLefschetz numbers of the fibration. 
472017  Stable pair PT invariants on smooth fibrations II

We study PandharipandeThomas’s stable pair theory on smooth K3 fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of KawaiYoshioka’s formula for the Euler characteristics of moduli spaces of stable pairs on K3 surfaces and NoetherLefschetz numbers of the fibration. 
4122017  Stable pair PT invariants on nodal fibrations: perverse sheaves, Wallcrossings, and an analog of fiberwise Tduality  Following lecture 4, we continue the study of stable pair invariants of K3fibered threefolds., We investigate the relation of these invariants with the perverse (noncommutative) stable pair invariants of the K3fibration. In the case that the fibration is a projective CalabiYau threefold, by means of wallcrossing techniques, we write the stable pair invariants in terms of the generalized DonaldsonThomas invariants of 2dimensional Gieseker semistable sheaves supported on the fibers. 
4142017  DT versus MNOP invariants and S_duality conjecture on general complete intersections  Motivated by Sduality modularity conjectures in string theory, we define new invariants counting a restricted class of twodimensional torsion sheaves, enumerating pairs Z⊂H in a Calabi–Yau threefold X. Here H is a member of a sufficiently positive linear system and Z is a onedimensional subscheme of it. The associated sheaf is the ideal sheaf of Z⊂H, pushed forward to X and considered as a certain Joyce–Song pair in the derived category of X. We express these invariants in terms of the MNOP invariants of X. 
4192017  Proof of Sduality conjecture on quintic threefold I  I will talk about an algebraicgeometric proof of the Sduality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic CalabiYau threefold. We use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity. More precisely, we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasiprojective surface is a modular form. This is a generalization of the result of OkounkovCarlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of NoetherLefschetz numbers as I will explain, will provide the ingredients to achieve an algebraicgeometric proof of Sduality modularity conjecture. 
4282017  Proof of Sduality conjecture on Quintic threefold II  I will talk about an algebraicgeometric proof of the Sduality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic CalabiYau threefold. We use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity. More precisely, we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasiprojective surface is a modular form. This is a generalization of the result of OkounkovCarlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of NoetherLefschetz numbers as I will explain, will provide the ingredients to achieve an algebraicgeometric proof of Sduality modularity conjecture. 
Titles, abstracts and schedule will be provided nearer to the event.
Dan Freed, UT Austin
Anton Kapustin, California Institute of Technology
Alexei Y. Kitaev, California Institute of Technology
Greg Moore, Rutgers University
Constantin Teleman, University of Oxford
Organizers:
Mike Hopkins, ShingTung Yau
* This event is sponsored by CMSA Harvard University.
Gerard Ben Arous, Courant Institute of Mathematical Sciences
Alex Bloemendal, Broad Institute
Arup Chakraburty, MIT
Zhou Fan, Stanford University
Alpha Lee, Harvard University
Matthew R. McKay, Hong Kong University of Science and Technology (HKUST)
David R. Nelson, Harvard University
Nick Patterson, Broad Institute
Marc Potters, Capital Fund management
Yasser Roudi, IAS
Tom Trogdon, UC Irvine
Organizers:
Michael Brenner, Lucy Colwell, Govind Menon, HorngTzer Yau
Schedule:
January 9 – Day 1  
9:30am – 10:00am  Breakfast & Opening remarks 
10:00am – 11:00am  Marc Potters, “Eigenvector overlaps and the estimation of large noisy matrices” 
11:00am – 12:00pm  Yasser Roudi 
12:00pm – 2:00pm  Lunch 
2:00pm  Afternoon Discussion 
January 10 – Day 2  
8:30am – 9:00am  Breakfast 
9:00am – 10:00am  Arup Chakraburty, “The mathematical analyses and biophysical reasons underlying why the prevalence of HIV strains and their relative fitness are simply correlated, and pose the challenge of building a general theory that encompasses other viruses where this is not true.” 
10:00am – 11:00am  Tom Trogdon, “On the average behavior of numerical algorithms” 
11:00am – 12:00pm  David R. Nelson, “NonHermitian Localization in Neural Networks” 
12:00pm – 2:00pm  Lunch 
2:00pm  Afternoon Discussion 
January 11 – Day 3  
8:30am – 9:00am  Breakfast 
9:00am – 10:00am  Nick Patterson 
10:00am – 11:00am  Lucy Colwell 
11:00am – 12:00pm  Alpha Lee 
12:00pm – 2:00pm  Lunch 
2:00pm4:00pm  Afternoon Discussion 
4:00pm  Gerard Ben Arous (Public Talk), “Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms“ 
January 12 – Day 4  
8:30am – 9:00am  Breakfast 
9:00am – 10:00am  Govind Menon 
10:00am – 11:00am  Alex Bloemendal 
11:00am – 12:00pm  Zhou Fan, “Free probability, random matrices, and statistics” 
12:00pm – 2:00pm  Lunch 
2:00pm  Afternoon Discussion 
January 13 – Day 5  
8:30am – 9:00am  Breakfast 
9:00am – 12:00pm  Free for Working 
12:00pm – 2:00pm  Lunch 
2:00pm  Free for Working 
* This event is sponsored by CMSA Harvard University.
The minischool will consist of lectures by experts in geometry and analysis detailing important developments in the theory of nonlinear equations and their applications from the last 2030 years. The minischool is aimed at graduate students and young researchers working in geometry, analysis, physics and related fields.
December 3rd – Day 1  
9:00am – 10:30am  Cliff Taubes, “Compactness theorems in gauge theories” 
10:45am – 12:15pm  Valentino Tosatti, “Complex MongeAmpère Equations” 
12:15pm – 1:45pm  LUNCH 
1:45pm – 3:15pm  Pengfei Guan, “MongeAmpère type equations and related geometric problems” 
3:30pm – 5:00pm  Jared Speck, “Finitetime degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations” 
December 4th – Day 2  
9:00am – 10:30am  Cliff Taubes, “Compactness theorems in gauge theories” 
10:45am – 12:15pm  Valentino Tosatti, “Complex MongeAmpère Equations” 
12:15pm – 1:45pm  LUNCH 
1:45pm – 3:15pm  Pengfei Guan, “MongeAmpère type equations and related geometric problems” 
3:30pm – 5:00pm  Jared Speck, “Finitetime degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations” 
Bong Lian (Brandeis University), SiuCheong Lau (Boston University), ShingTung Yau (Harvard University)
Please click Workshop Program for a downloadable schedule with talk abstracts.
Monday, November 28 – Day 1  
10:30am –11:30am  Hiro Lee Tanaka, “Floer theory through spectra” 
Lunch  
1:00pm – 2:30pm  Fabian Haiden, “Categorical Kahler Geometry” 
2:30pm2:45pm  Break 
2:45pm – 4:15pm  Fabian Haiden, “Categorical Kahler Geometry” 
4:30pm – 5:15pm  Garret Alston, “Potential Functions of Nonexact fillings” 
Tuesday, November 29 – Day 2  
10:30am –11:30am  Conan Leung, “Remarks on SYZ” 
Lunch  
1:00pm – 2:30pm  Jingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants” 
2:30pm2:45pm  Break 
2:45pm – 4:15pm  Hiro Lee Tanaka, “Floer theory through spectra” 
4:30pm – 5:15pm  Hansol Hong, “Mirror Symmetry for punctured Riemann surfaces and gluing construction” 
Wednesday, November 30 – Day 3  
10:30am –11:30am  Junwu Tu, “Homotopy Linfinity spaces and mirror symmetry” 
Lunch  
1:00pm – 2:30pm  Jingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants” 
2:302:45pm  Break 
2:45pm – 4:15pm  David Treumann, “Invariants of Lagrangians via microlocal sheaf theory” 
Thursday, December 1 – Day 4  
10:30am –11:30am  David Treumann, “Some examples in three dimensions” 
Lunch  
1:00pm – 2:30pm  Junwu Tu, “Homotopy Linfinity spaces and mirror symmetry” 
2:302:45pm  Break 
2:45pm – 3:30pm  Netanel Blaier, “The quantum Johnson homomorphism, and the symplectic mapping class group of 3folds” 
* This event is sponsored by the Simons Foundation and CMSA Harvard University.
Date  Name  Title/Abstract 
021517  Lisa Hartung, Courant Institute 
Title: The Structure of Extreme Level Sets in Branching Brownian Motion Abstract: Branching Brownian motion (BBM) is a classical process in probability, describing a population of particles performing independent Brownian motion and branching according to a Galton Watson process. Arguin et al.\ and A\”\i{}d\’ekon et al.\ proved the convergence of the extremal process. In the talk we discuss how one can obtain finer results on the extremal level sets by using a random walklike representation of the extremal particles. We establish among others the upper tail probabilities for the distance between the maximum and the second maximum (joint work with Aser Cortines and Oren Louder). 
022217  Bob Hough, Stony Brook University 
Title: Random walk on unipotent groups Abstract: I will describe results of two recent papers from random walk on unipotent groups. In joint work with Diaconis (Stanford), we obtain a new local limit theorem on the real Heisenberg group, and determine the mixing time of coordinates for some random walks on finite unipotent groups. In joint work with Jerison and Levine (Cornell) we prove a cutoff phenomenon in sandpile dynamics on the torus $(\mathbb{Z}/m\mathbb{Z})^2$ and obtain a new upper bound on the critical exponent of sandpiles on $\mathbb{Z}^2$. 
030117  Shirshendu Ganguly, UC Berkeley  Title: Large deviation and counting problems in sparse settings
Abstract: The upper tail problem in the Erd ̋osR ́enyi random graph G ∼ Gn,p, where every edge is included independently with probability p, is to estimate the probability that the number of copies of a graph H in G exceeds its expectation by a factor 1 + δ. The arithmetic analog considers the count of arithmetic progressions in a random subset of Z/nZ, where every element is included independently with probability p. In this talk, I will describe some recent results regarding the solution of the upper tail problem in the sparse setting, i.e. where p decays to zero, as n grows to infinity. The solution relies on nonlinear large deviation principles developed by Chatterjee and Dembo and more recently by Eldan and solutions to various extremal problems in additive combinatorics. 
030817  Xiaoqin Guo, Purdue University  Title: Harnack inequality for a balanced random environment
Abstract: We consider a random walk in a balanced random environment on $Z^d$ which is allowed to be nonelliptic. This is a Markov chain generated by a discrete nondivergence form operator. In this talk, assuming that the environment is iid and “genuinely ddimensional”, we will present a Harnack inequality for discrete harmonic functions of the corresponding operator. The result is based on the analysis of the percolation structure of the (nonreversible) environment and renormalization arguments. Joint work with N. Berger, J.D. Deuschel and M.Cohen. 
031517  Chiranjib Mukherjee, New York University  POSTPONED DUE TO WEATHER 
032217  Alexander Fribergh, University of Montreal  Title: The ant in the labyrinth
Abstract: One of the most famous open problem in random walks in random environments is to understand the behavior of a simple random walk on a critical percolation cluster, a model known as the ant in the labyrinth. I will present new results on the scaling limit for the simple random walk on the critical branching random walk in high dimension. In the light of lace expansion, we believe that the limiting behavior of this model should be universal for simple random walks on critical structures in high dimensions. 
032417  Chiranjib Mukerjee, Courant Institute  Title: Compactness and Large Deviations
Abstract: In a reasonable topological space, large deviation estimates essentially deal with probabilities of events that are asymptotically (exponentially) small, and in a certain sense, quantify the rate of these decaying probabilities. In such estimates, upper bounds for such small probabilities often require compactness of the ambient space, which is often absent in problems arising in statistical mechanics (for example, distributions of local times of Brownian motion in the full space Rd). Motivated by such a problem, we present a robust theory of “translationinvariant compactication” of probability measures in Rd. Thanks to an inherent shiftinvariance of the underlying problem, we are able to This talk is based on joint works with S. R. S. Varadhan (New York), as well as with Erwin Bolthausen (Zurich) and Wolfgang Koenig (Berlin). 
032917  Nina Holden, MIT  Title: Percolationdecorated triangulations and their relation with SLE and LQG
Abstract: The SchrammLoewner evolution (SLE) is a family of random fractal curves, which is the proven or conjectured scaling limit of a variety of twodimensional lattice models in statistical mechanics, e.g. percolation. Liouville quantum gravity (LQG) is a model for a random surface which is the proven or conjectured scaling limit of discrete surfaces known as random planar maps (RPM). We prove that a percolationdecorated RPM converges in law to SLEdecorated LQG in a certain topology. This is joint work with Bernardi and Sun. We then discuss a work in progress where we try to strengthen the topology of convergence of a RPM to LQG by considering conformal embeddings of the RPM into the complex plane. This is joint work with Sun and with Gwynne, Miller, Sheffield, and Sun.
NOTE: This talk will be held in room G02 
040517  Steven Heilman, UCLA  Title: Noncommutative Majorization Principles and Grothendieck’s Inequality
Abstract: The seminal invariance principle of MosselO’DonnellOleszkiewicz implies the following. Suppose we have a multilinear polynomial Q, all of whose partial derivatives are small. Then the distribution of Q on i.i.d. uniform {1,1} inputs is close to the distribution of Q on i.i.d. standard Gaussian inputs. The case that Q is a linear function recovers the BerryEsseen Central Limit Theorem. In this way, the invariance principle is a nonlinear version of the Central Limit Theorem. We prove the following version of one of the two inequalities of the invariance principle, which we call a majorization principle. Suppose we have a multilinear polynomial Q with matrix coefficients, all of whose partial derivatives are small. Then, for any even K>1, the Kth moment of Q on i.i.d. uniform {1,1} inputs is larger than the Kth moment of Q on (carefully chosen) random matrix inputs, minus a small number. The exact statement must be phrased carefully in order to avoid being false. Time permitting, we discuss applications of this result to anticoncentration, and to computational hardness for the noncommutative Grothendieck inequality. (joint with Thomas Vidick) 
041217 
Oanh Nguyen, Yale University 
Title: Roots of random polynomials Abstract: Random polynomials, despite their simple appearance, remain a mysterious object with a large number of open questions that have attracted intensive research for many decades. In this talk, we will discuss some properties of random polynomials including universality and asymptotic normality. I will also talk about some interesting open questions. The talk is based on joint works with Yen Do, Hoi Nguyen, and Van Vu. Note: This talk will take place from 2:003:00pm 
041217  Subhajit Goswami, University of Chicago 
Title: Liouville firstpassage percolation and Watabiki’s prediction Abstract: In this talk I will give a brief introduction to Liouville firstpassage percolation (LFPP) which is a model of random metric on a finite planar grid graph. It was studied primarily as a way to make sense of the random metric associated with Liouville quantum gravity (LQG), one of the major open problems in contemporary probability theory. I will discuss some recent results on this metric and the main focus will be on estimates of the typical distance between two points. I will also discuss about the apparent disagreement of these estimates with a prediction made in the physics literature about LQG metric. The talk is based on a joint work with Jian Ding. 
041917  Weijun Xu, University of Warwick  Title: Meaing of infinities in KPZ and Phi^4_3
Abstract: Many interesting stochastic PDEs arising from statistical physics are illposed in the sense that they involve products between distributions, so the solutions to these equations are obtained after renormalisations, which typically change the original equation by a quantity that is infinity. I will use KPZ and Phi^4_3 as two examples to explain the meanings of these infinities. As a consequence, we will see how these two equations, interpreted after suitable renormalisations, arise naturally as (weakly) universal limits for two distinct classes of systems. Part of the talk based on joint works with Martin Hairer, Cyril Labbe and Hao Shen. 
042617  Ashkan Nikeghbali, University of Zurich  
050317  Ilya Soloveychik, Harvard University/Hebrew University of Jerusalem  Title: Deterministic Random Matrices
Abstract: In many applications researchers and engineering need to simulate random symmetric sign (+/1) matrices (Wigner’s matrices). The most natural way to generate an instance of such a matrix is to toss a fair coin, fill the upper triangular part of the matrix with the outcomes and reflect it part into the lower triangular part. For large matrix sizes such approach would require a very powerful source of randomness due to the independence condition. In addition, when the data is generated by a truly random source, atypical nonrandom looking outcomes have nonzero probability of showing up. Yet another issue is that any experiment involving tossing a coin would be impossible to reproduce exactly, which may be crucial in computer scientific applications. In this talk we focus on the problem of generating n by n symmetric sign matrices based on the similarity of their spectra to Wigner’s semicircular law. We develop a simple completely deterministic construction of symmetric sign matrices whose spectra converge to the semicircular law when n grows to infinity. The Kolmogorov complexity of the proposed algorithm is as low as 2 log (n) bits implying that the real amount of randomness conveyed by the semicircular property is quite small. 
Date  Name  Title 
092116  Stephane Benoist, MIT  Title: Near critical spanning forests
Abstract: We study random spanning forests in the plane, which are slight perturbations of a uniformly chosen spanning tree (UST) and come with a natural fragmentation dynamics. We show how to relate the scaling limit of these forests to the stationary distribution of a natural Markov process on a state space of abstract graphs with edgeweights. This abstract graph setup could be fruitful for using renormalization ideas. In this point of view, our dynamics on forest corresponds to a repulsive direction around the UST fixed point. This is a joint work with Laure Dumaz (CNRS, ParisDauphine) and Wendelin Werner (ETH Zürich). 
092816  Antonio Auffinger, Northwestern 
Title: Parisi formula for the ground state energy of the SherringtonKirkpatrick model Abstract: Spin glasses are disordered spin systems originated from the desire of understanding strange magnetic behaviors of certain alloys in physics. As mathematical objects, they are often cited as examples of complex systems and have provided several fascinating structures and conjectures. In this talk, we will focus on the SherringtonKirkpatrick spin glass model. We will present the Parisi formula and some properties for the maximum energy. In addition, we will discuss some representations of the Parisi Formula in terms of stochastic optimal control problems. This talk is based on recent joint works with WeiKuo Chen. 
100516  Edgar Dobriban, Stanford 
Title: Computation, statistics and random matrix theory Abstract: Random matrices are useful models for large datasets. The MarchenkoPastur (1967) ensemble for general covariance matrices is an increasingly used modeling framework that captures the effects of correlations in the data, with numerous statistical applications. In this talk we discuss the fruitful interactions between computation, statistics and random matrix theory in this area. We explain a fundamental computational problem in RMT: computing the limit empirical spectral distribution (ESD) of general covariance matrices. Our recent Spectrode method solves this problem efficiently. As an application, we solve a challenging problem in theoretical statistics. We construct optimal statistical tests based on linear spectral statistics to detect principal components below the phase transition. We also describe the software we are building for working with large random matrices, which we hope will broaden reach of RMT. 
101216  Michael Damron, Georgia Tech  Title: Bigeodesics in firstpassage percolation
Abstract: In firstpassage percolation, we place i.i.d. continuous weights at the edges of Z^2 and consider the weighted graph metric. A distance minimizing path between points x and y is called a geodesic, and a bigeodesic is a doublyinfinite path whose segments are geodesics. It is a famous conjecture that almost surely, there are no bigeodesics. In the `90s, Licea and Newman showed that, under a curvature assumption on the “asymptotic shape,” all infinite geodesics have asymptotic directions and there are no bigeodesics with both ends directed in some deterministic subset D of [0,2pi) with countable complement. I will discuss recent work with Jack Hanson in which we show that there are no bigeodesics with one end directed in any deterministic direction, assuming the shape boundary is differentiable. This rules out existence of ground state pairs for the related disordered ferromagnet whose interface has a deterministic direction. Furthermore it resolved the BenjaminiKalaiSchramm “midpoint problem” under the additional assumption of differentiability. 
101916 
Dmitry Panchenko, University of Toronto

Title: Free energy in the nonhomogeneous SK model and SK model with vector spins. Abstract: I will describe some ideas behind the Parisi formula for the free energy in the classical SherringtonKirkpatrick model and explain how these ideas can be extended to compute the free energy in two versions of the model: (a) with nonhomogeneous interactions and (b) with vector spins, for example, the Potts spin glass. 
102416 (Monday!)  Sebastien Bubeck, Microsoft 
Title: Local maxcut in smoothed polynomial time Abstract: The local maxcut problem asks to find a partition of the vertices in a weighted graph such that the cut weight cannot be improved by moving a single vertex (that is the partition is locally optimal). This comes up naturally, for example, in computing Nash equilibrium for the party affiliation game. It is wellknown that the natural local search algorithm for this problem might take exponential time to reach a locally optimal solution. We show that adding a little bit of noise to the weights tames this exponential into a polynomial. In particular we show that local maxcut is in smoothed polynomial time (this improves the recent quasipolynomial result of Etscheid and Roglin). Joint work with Omer Angel, Yuval Peres, and Fan Wei. 
102616  Wei Wu, NYU 
Title: Extremal and local statistics for gradient field models Abstract: The gradient field models with uniformly convex potential (also known as the GinzburgLandau field) is believed to be in the Gaussian universality class, and has been applied to study different lattice models. Previous work by NaddafSpencer and by Miller proved the macroscopic averages of the field converge to a continuum Gaussian free field. In this talk we will describe recent progresses to understand the maximum and local statistics of the field, that indicates the Gaussian universality holds in a strong sense. 
110216 
Ramon van Handel, Princeton 
Title: Inhomogeneous random matrices Abstract: How do random matrices behave when the entries can have an arbitrary variance pattern? New problems arise in this setting that are almost completely orthogonal to classical random matrix theory. I will illustrate such problems by describing one of my favorite conjectures on this topic due to R. Latala, and the various mathematical techniques and questions that are emerging from its investigation. 
110916
TIME CHANGE: 2:50PM 
TITLE: Computational Bayesianism, sums of squares, cliques, and unicorns ABSTRACT: Can we make sense of quantities such as “the probability that 2^81712357 – 1 is prime” or “the probability that statement X is a logical contradiction”? More generally, can we use probabilities to quantify our “computational uncertainty” in cases where all the relevant information is given but in a computationally hardtoextract form? In this talk we will discuss how such “pseudo probabilities” can arise from the Sum of Squares (SOS) semidefinite program (Parrilo’00, Lasserre’01). We will show how this yields an approach for showing both positive and negative results for the SOS algorithms. In particular we will present better algorithms for the tensor decomposition problem from data analysis, and stronger lower bounds for the planted clique problem. The talk will be partially based on joint works with Sam Hopkins, Jon Kelner, Pravesh Kothari, Ankur Moitra, Aaron Potechin and David Steurer. I will not assume any prior knowledge on the sum of squares algorithm or semidefinite programming. 

111616  Yu Gu, Stanford
TIME CHANGE: 2:30PM 
Title: Local vs global random fluctuations in stochastic homogenization Abstract: We will discuss stochastic homogenization of elliptic equations in divergence form, of which the probabilistic counterpart is the random conductance model. I will try to explain some probabilistic and analytic approaches we use to obtain the first and higher order random fluctuations. It turns out that in high dimensions, a formal twoscale expansion only leads to the correct “local” fluctuation, but not the “global” one. Part of the talk is based on joint work with JeanChristophe Mourrat. 
112216
NOTE Date Change: Tuesday 
Jafar Jafarov, Stanford 
Title: SU(N) Wilson loop expectations Abstract: Lattice gauge theories are discrete approximations to quantum YangMills theories. The main object of interest in lattice gauge theories are Wilson loop expectations. I will present 1/N expansion for SU(N) Wilson loop expectations in strongly coupled SU(N) lattice gauge theory in any dimension. I will show how to represented the coefficients of the expansion as absolutely convergent sums over trajectories in a string theory on the lattice, establishing a kind of gaugestring duality. 
113016
ROOM CHANGE: G02 
James Lee, University of Washington 
TITLE: Conformal growth rates, spectral geometry, and distributional limits of graphs ABSTRACT: Given a graph, one can deform its geometry according to a function that assigns nonnegative weights to the vertices. We refer to this as a “conformal” deformation of the graph metric. For a finite graph, it makes sense to define the area of such a weight as the average of the squared weights of the vertices. One can similarly define the area of a conformal weight for a unimodular random graph. The conformal growth exponent is the smallest rate of volume growth of balls achievable by a conformal weight of unit area. We show that if a unimodular (rooted) random graph (G,x) has quadratic conformal growth (QCG) and the law of deg(x) is sufficiently wellbehaved, then the random walk on G is almost surely recurrent. We also argue that our joint with Kelner, Price, and Teng (2011) can be used to show that every distributional limit of finite planar graphs has QCG. More generally, this holds for Hminorfree graphs, and other interesting families like string graphs (the intersection graph of continuous arcs in the plane). These methods do not rely on circle packings, and can instead be thought of as directly uniformizing the underlying graph metric. They yield a short proof of Benjamini and Schramm’s result that a distributional limit of finite, boundeddegree planar graphs is almost surely recurrent, and provide a positive answer to their conjecture that the same should hold for Hminorfree graphs. GurelGurevich and Nachmias recently solved a central open problem by showing that the uniform infinite planar triangulation (UIPT) and quadrangulation (UIPQ) are almost surely recurrent. By combining QCG with methods from spectral geometry, we present a new proof of this fact that follows from strong quantitative bounds on the heat kernel. A similar phenomenon holds beyond dimension two: Assuming the law of deg(x) has tails that decay faster than any inverse polynomial, the almost sure spectral dimension of a unimodular random graph (G,x) is equal to its conformal growth exponent. This has consequences for limits of graphs that can be spherepacked in R^d for d > 2. 
120716  Dan Romik, UC Davis 
Title: A Pfaffian point process for Totally Symmetric Self Complementary Plane Partitions Abstract: Totally Symmetric Self Complementary Plane Partitions (TSSCPPs) can be encoded as a family of nonintersecting lattice paths having fixed initial points and variable endpoints. The endpoints of the paths associated with a uniformly random TSSCPP of given order therefore induce a random point process, which turns out to be a Pfaffian point process. I will discuss conjectural formulas for the entries of the correlation kernel of this process, and a more general “rationality phenomenon”, which if true implies the existence of an interesting limiting process describing “infinite TSSCPPs” as well as conjectural probabilities for the occurrence of certain connectivity patterns in loop percolation (a.k.a. the dense O(1) loop model). 
121416  Brian Rider, Temple 
Title: Universality for the random matrix hard edge Abstract: The hard edge refers to the distribution of the smallest singular value for certain ensembles of random matrices, or, and what is the same, that of the minimal point of a logarithmic gas constrained to the positive half line. For any inverse temperature and “quadratic” potential the possible limit laws (as the dimension, or number of particles, tends to infinity) was characterized by Jose Ramirez and myself in terms of the spectrum of a (random) diffusion generator. Here we show this picture persists for more general convex polynomial potentials. Joint work with Patrick Waters. 
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