Timing: Spring 2016
Abstract: Calogero-Moser-Sutherland many-body systems arose originally in the 1970’s simultaneously in Nuclear Physics, Mathematical Physics and Solid State Physics. Since then they were found in some incarnations in diverse branches of physics and mathematics such as the theory of quantum Hall effect, Yang-Mills and Chern-Simons gauge theories in various dimensions with various amounts of supersymmetry, noncommutative geometry, topology of Hilbert schemes, geometric representation theory, Gromov-Witten invariants, theory of symmetric functions, SLE, Random Matrix theory, collective field theory and random geometries.
The aim of the seminar series is to review and explore these connections.
Spring 2016 Lectures:
Date | Time | Title | Speaker |
Jan. 20 | 2:30 pm | Quivers and qq-characters | Nikita Nekrasov |
Jan. 27 | 2:30 pm | 6 vertex quantum integrable system and cohomology of Grassmanian | Vassily Gorbounov |
Mar. 9 | 2:30 pm | Field Generalizations of the Calogero-Moser System | Igor Krichever |
Mar. 16 | 2:30 pm | Metrics of constant positive curvature with conical singularities. | Alexandre Eremenko (Purdue) |
Mar. 23 | 2:30 pm | ||
Mar. 30 | 2:30 pm | ||
Fall 2015, Location Math Tower 5-127 or SCGP 313, Thursday 1PM:
(09/03/2015) | Michael Sullivan, UMass (Amherst) | Legendrian invariants constructed using regular cell decompositions of surfaces, |
(09/10/2015) | N/A | N/A |
(09/17/2015) | Kenji Fukaya, Simons Center, Stony Brook | SO(3)-Floer homology of 3-manifolds with boundary |
(09/24/2015) | Marco Farinati, Universidad de Buenos Aires | Link and knot invariants from colorings and 2-cocycles |
(10/01/2015) | Chris Woodward, Rutgers University | Fukaya categories and the minimal model program: creation and survival |
(10/08/2015) | Jean Gutt | N/A |
(10/15/2015) | Penka Georgieva | Real Gromov-Witten theory in all genera |
(10/22/2015) | Adam Levine (Princeton) | Khovanov homology and knot Floer homology for pointed links |
(10/29/2015) | N/A | N/A |
(11/05/2015) | Cagatay Kutluhan | N/A |
(11/12/2015) | TBA | TBA |
(11/19/2015) | ||
(12/03/2015) | ||
(12/10/2015) |
Organized by Sasha Abanov, Tankut Can, Anton Kapustin, and Paul Wiegmann
April 18, 2016 – June 17, 2016
The quantum Hall effect (QHE) is a fascinating and important phenomenon. Since its experimental discovery in the early 80’s the QHE continues to fuel work in experimental physics, metrology, fundamental theoretical physics and mathematics.
At very low temperatures and strong magnetic fields, highly entangled collective electronic quantum states are formed on surfaces of ultra clean doped semiconductors. Despite varying microscopic details and imperfections of materials, these states possess universal properties demonstrating very precise (up to 9 significant digits) quantization of the Hall conductivity in units of fundamental constants. Other observable features are: an excitation gap determined by electron interactions, fractional charge and statistics of elementary excitations, and chiral massless boundary modes with universal dynamics.
Many universal features of the QHE are also captured at the microscopic scale by model electron wave functions. An outstanding theoretical task is to connect this microscopic description with the macroscopic picture discussed above.
Recently, the physics of low energy transport phenomena has been connected to the response of the ground state to variations of the spatial geometry. This observation has led to a geometric description of QHE states, which links the physics of QH states to problems of modern geometry (Kahler geometry). Another rapidly developing link is a relation between the FQHE and the theory of random geometry and quantum gravity. The synthesis of subjects and intriguing links to modern mathematics give the QHE a very special status.
The goal of the program is to bring together physicists and mathematicians working on topics related to the geometry of QH states, in order to develop a geometric approach to quantum Hall states. The program will also encourage a broader discussion of the role of geometry in quantum states of condensed matter systems. Some of the key topics of the program are:
Speaker and Seminar Schedule:
The weekly talks take place on Mondays, Wednesday and Fridays at 10:30am in room 313.
Date and Time | Title | Presenters |
4/25 at 10:30am – Room 313 | Galilean invariance at quantum Hall edge | Sergej Moroz |
4/27 at 10:30am – Room 313 | Towards the classification of gapped phases of matter | Ryan Thorngren |
4/29 at 10:30am – Room 313 | Non-commutative geometry techniques for aperiodic condensed matter systems | Emil Prodan |
5/2 at 10:30am – Room 313 | Geometric deformation and Berry curvature in quantum Hall states | Barry Bradlyn |
5/4 at 10:30am – Room 313 | The holographic Weyl semi-metal | Karl Landsteiner |
5/4 at 1:00pm – Room 313 | Mathematical physics of map enumeration | Peter Zograf |
5/6 at 10:30am – Room 313 | Electromagnetic response of semimetals from wavefunction geometry and topology | Joel Moore |
5/9 at 10:30am – Room 313 | CANCELLED | |
5/10 at 10:30am – Room 313 | Hall viscosity from Hall conductivity in Dirac crystals | Maria A. H. Vozmediano |
5/11 at 10:30am – Room 313 | Anyons from braiding fluxes in the Pauli Hamiltonian | Yosi Avron |
5/13 at 10:30am – Room 313 | CANCELLED | |
5/16 at 10:30am – Room 313 | The Nematic Fractional Quantum Hall State and the interplay of Geometry and Topology | Eduardo H Fradkin |
5/18 at 10:30am – Room 313 | Geometric Defects in FQH states | Andrey Gromov |
5/20 at 10:30am – Room 313 | CANCELLED | |
5/23 at 10:30am – Room 313 | Fractional Quantum Hall Effect on Singular Surfaces | Misha Laskin |
5/25 at 10:30am – Room 313 | Hydrodynamics with non-Abelian currents: from spin Hall effect to quark-gluon plasma | Piotr Surowka |
5/26 at 2:00pm – Room 313 | Particle Formation and Ordering in Strongly Correlated Fermionic Systems: Solving a Model of Quantum Chromodynamics | Alexei Tsvelik |
5/27 at 10:30am – Room 313 | Absolute Stability without Topological Order | Shivaji Sondhi |
6/1 at 10:30am – Room 313 | Jack Polynomials as Quantum Hall States | Boris Hanin |
6/3 at 10:30am – Room 313 | Questions around Laughlin states on Riemann surfaces | Semyon Klevtsov |
6/6 at 10:30am – Room 313 | CANCELLED | |
6/8 at 10:30am – Room 313 | Questions around Laughlin states on Riemann surfaces, part 2 | Semyon Klevtsov |
6/10 at 10:30am – Room 313 | Hydrodynamics with Hall viscosity: variational approach | Alexander Abanov |
6/13 at 10:30am – Room 313 | CANCELLED | |
6/15 at 10:30am – Room 313 | Newton-Cartan geometry and hydrodynamics with Hall viscosity | Gustavo Monteiro |
6/16 at 1:30pm – Room 313 | Formalism for the solution of quadratic Hamiltonians with large cosine terms | Sriram Ganeshan |
6/17 at 10:30am – Room 313 | Quasi-electrons on the sphere and jack polynomials | Boris Hanin |
Organized by Mark de Cataldo, Radu Laza, Christian Schnell
March 7, 2016 – April 29, 2016
Hodge theory is a very powerful tool for understanding the geometry of complex algebraic varieties and it has a wide range of applications in complex and algebraic geometry, mirror symmetry, representation theory, combinatorics, etc. This program focuses on different aspects of Hodge theory, their applications in algebraic geometry and related areas and, very importantly, on their interactions. We plan to cover the following four themes:
(1) p-adic Hodge theory and arithmetic geometry
(2) mixed Hodge modules and their applications
(3) log geometry, with an emphasis on degenerations and moduli problems
(4) applications of Hodge theory to questions about algebraic cycles
There will be four lecture series, “Hitchin systems and Hodge theory” (R. Donagi and T. Pantev), “p-adic Hodge theory” (B. Bhatt), “Log geometry and log Hodge structures” (M. Olsson), and “Mixed Hodge modules” (Ch. Schnell), a weekly seminar, and several mini-courses.
Date | Time | Title | Speaker | Location |
Tues. March 8 | 2:15 pm | Higgs bundles, T-duality, and Hodge theory | Tony Pantev | SCGP 313 |
Wed. March 9 | 1:00 pm | The Lefschetz (1,1) theorem for a singular variety. | Donu Arapura | SCGP 313 |
Wed. March 9 | 4:00 pm | Rota’s conjecture for matroids via toric varieties | Mircea Mustata | Math P131 |
Thurs. March 10 | 11:30 am | Classifying spaces of degenerating mixed Hodge structures, IV:The fundamental diagram (with Kazuya Kato, Chikara Nakayama) |
Sampei Usui | SCGP 313 |
Thurs. March 10 | 2:00 pm | Higgs bundles, T-duality, and Hodge theory | Tony Pantev | SCGP 313 |
Date | Time | Title | Speaker | Location |
Tues. March 15 | 2:00 pm | Introduction to mixed Hodge modules 1 | Christian Schnell | SCGP 313 |
Thurs. March 17 | 2:00 pm | Introduction to mixed Hodge modules 2 | Christian Schnell | SCGP 313 |
Mini-Workshop on Moduli and Hodge Theory: https://services.math.duke.edu/~robles/FRGw6/schedule.html
Date | Time | Title | Speaker | Location |
Tues. March 22 | 2:15 pm | Introduction to Mixed Hodge Modules 3 | Claude Sabbah | SCGP 313 |
Wed. March 23 | 1:00 pm | Introduction to Mixed Hodge Modules 4 | Claude Sabbah | SCGP 313 |
Wed. March 23 | 4:00 pm | Complex varieties with infinite Chow groups modulo 2 | Burt Totaro | Math P131 |
Thurs. March 24 | 11:30 am | Generic vanishing and minimal cohomology classes on abelian fivefolds | Stefan Schreieder | SCGP 313 |
Thurs. March 24 | 2:00 pm | Introduction to Mixed Hodge Modules 5 | Christian Schnell | SCGP 313 |
Date | Time | Title | Speaker | Location |
Tues. March 29 | 2:15 pm | Introduction to Mixed Hodge Modules 6 | Christian Schnell | SCGP 313 |
Tues. March 29 | 4:00 pm | Some aspects of Lefschetz theorems in algebraic geometry | Hélène Esnault | SCGP 313 |
Wed. March 30 | 1:00 pm | Examples of Maximally Degenerate Curves and Surfaces | Mark Green | SCGP 313 |
Wed. March 30 | 4:00 pm | On descending cohomology geometrically | Charles Vial | Math P131 |
Thurs. March 31 | 11:30 am | Moduli and Periods | Phillip Griffiths | SCGP 313 |
Thurs. March 31 | 2:00 pm | Introduction to Mixed Hodge Modules 7 | Claude Sabbah | SCGP 313 |
Date | Time | Title | Speaker | Location |
Tues. April 5 | 2:15 pm | Hitchin Systems, Geometric Langlands, and Hodge Theory | Ron Donagi | SCGP 313 |
Tues. April 5 | 4:00 pm | Transcendental Hodge algebra and some conjectures | Misha Verbitsky | SCGP 313 |
Wed. April 6 | 1:00 pm | Hitchin Systems, Geometric Langlands, and Hodge Theory | Ron Donagi | SCGP 313 |
Wed. April 6 | 4:00 pm | Hodge theory and Gromov-Witten invariants | Dave Morrison | Math P131 |
Thurs. April 7 | 11:30 am | On hyperplane sections of K3 surfaces | Andrea Bruno | SCGP 313 |
Thurs. April 7 | 2:00 pm | Constructing algebraic cycles on products of K3 surfaces via hyperholomorphic bundles | Eyal Markman | SCGP 313 |
Date | Time | Title | Speaker | Location |
Tues. April 12 | 2:15 pm | Log geometry and log Hodge structures | Martin Olsson | SCGP 313 |
Tues. April 12 | 4:00 pm | Hodge Groups of Hodge Structures with Hodge Numbers (n,0,…,0,n) | Laure Flapan | SCGP 313 |
Wed. April 13 | 1:00 pm | Fake tori | Zhiyu Tian | SCGP 313 |
Wed. April 13 | 4:00 pm | The Miyaoka-Yau inequality for minimal models of general type and ball quotients | Behrouz Taji | Math P131 |
Thurs. April 14 | 11:30 pm | Cycle transversal Mumford-Tate domains associated to period domains | Ana-Maria Brecan | SCGP 313 |
Thurs. April 14 | 2:00 pm | Log geometry and log Hodge structures | Martin Olsson | SCGP 313 |
Date | Time | Title | Speaker | Location |
Tues. April 19 | 2:15 pm | p-adic Hodge theory | Bhargav Bhatt | SCGP 313 |
Wed. April 20 | 2:00 pm | Log geometry and log Hodge structures | Martin Olsson | SCGP 313 |
Wed. April 20 | 4:00 pm | Hodge ideals | Mihnea Popa | Math P131 |
Thurs. April 21 | 11:30 am | Log geometry and log Hodge structures | Martin Olsson | SCGP 313 |
Thurs. April 21 | 2:00 pm | p-adic Hodge theory | Bhargav Bhatt | SCGP 313 |
Date | Time | Title | Speaker | Location |
Tues. April 26 | 2:15 pm | p-adic Hodge theory | Bhargav Bhatt | SCGP 313 |
Wed. April 27 | 4:00 pm | Iitaka’s conjecture over abelian varieties | Christian Schnell | Math P131 |
Thurs. April 28 | 11:30 am | K3 surfaces and complex multiplication | Madhav Nori | SCGP 313 |
Thurs. April 28 | 2:00 pm | p-adic Hodge theory | Bhargav Bhatt | SCGP 313 |
Organized by Pavel Bleher, Vladimir Korepin, and Bernard Nienhuis
February 15 – April 15, 2016
The purpose of the program is to relate physics and mathematics, and more specifically, statistical mechanics, algebraic combinatorics, and random matrices. The program will focus on the six-vertex model of statistical mechanics and related models, such as the XXZ spin chain, and loop models. The six-vertex model was introduced by Pauling in 1935mas a two dimensional version of a model for the hydrogen bonds in ice.
The bulk free energy and entropy in the six-vertex model were explicitly calculated for periodic boundary conditions by Lieb. Then other boundary conditions were studied. A very interesting case is the domain wallboundary conditions (DWBC). The six-vertex model provides an important ‘counterexample’ in statistical mechanics: the bulk free energy in the thermodynamic limit depends on boundary conditions. In particular, it is different for periodic and domain wall boundary conditions.
The partition function of the six-vertex model with DWBC in a finite box has been expressed, via the Yang-Baxter equations, in terms of a Hankel determinant. It can be furthermore expressed as a partition function of an ensemble of random matrices with a non-polynomial interaction. This expression was used via the powerful Riemann-Hilbert approach, the asymptotic behavior of the partition function of the six-vertex model with DWBC in different phase regions.
A remarkable observation was made by Razumov and Stroganov that concerns the six-vertex model at a special value of the parameter Delta=1/2, on afinite square grid, transformed into a loop model, i.e. a model of paths on the lattice that can end only on the boundary. In this case the paths visit all vertices exactly once, and all possible configurations are equally probable. This simple measure induces a probability measure on how the edges on the boundary are pairwise connected to each other. This is compared with another loop model placed on a half-infinite cylinder. In this case it is a loop model where the paths pass every edge once, every vertex twice and do not intersect. An equivalent six-vertex model has Delta=-1/2. Again every configuration is equally probable, and again this induces a probability measure on a pairing of the boundary edges. The observation of Razumov and Stroganov is that both probability measures of pairings of boundary edges are the same.
This observation was later proven by Cantini and Sportiello. The original observation has many generalizations on different geometries, but these have not been proven.
The six-vertex model with DWBC relates statistical mechanics to various problems of combinatorics: the statistics of alternating sign matrices, domino tilings, limiting shapes, nonintersecting lattice paths, loop models, and others. Limiting shape formulae in the six-vertex model were proposed recently. The six-vertex model has various generalizations to the eight-vertex model, higher-spin systems, coloring of a lattice, and others, which are important for applications. We plan on inviting leading experts, both physicists and mathematicians, workingon the combinatorics of six-vertex model and its generalizations.
All program talks are held in SCGP Seminar Room 313.
Date & Time | Speaker | Title |
2/15 at 2pm | Fabio Franchini | Spontaneous ergodicity breaking in invariant matrix models |
2/19 at 1pm | Bernard Nienhuis | Polynomial qKZ equations for loop models |
Date & Time | Speaker | Title |
2/22 at 2pm | Ramis Movassagh | A New Class of Exactly Solvable Quantum Spin Chain models |
2/22 at 1pm | Nikolay Bogoliubov | Random walks, plan partitions and correlation functions of Heisenberg chain in the limiting cases |
Date & Time | Speaker | Title |
2/29 at 2pm | Alexei Tsvelik | SU(2n) -invariant spin ladder as a perturbed integrable theory |
3/4 at 1pm | Gernot Akemann | Products of random matrices – exact solution and universality |
Date & Time | Speaker | Title |
3/7 at 2pm | Senya Shlosman | Roughening and ballistic transitions in the interacting dimers |
3/9 at 10:30am | Soichi Okada | Pfaffian identities and Schur’s Q-functions |
3/11 at 1pm | Barry McCoy | The Once and Future Ising Model |
Date & Time | Speaker | Title |
3/21 at 2pm | Robert Shrock | Some Results on Chromatic and Potts/Tutte Polynomials including Zeros and Asymptotic Limits for Families of Graphs |
3/25 at 1pm | Pavel Bleher | The mother body phase transition in the normal random matrix model |
Date & Time | Speaker | Title |
3/28 at 2pm | Ivan Kostov | Izergin-Korepin determinant, clustering and Sutherland limit |
4/1 at 1pm | Olof Salberger | Shor—Movassagh Model at Half Integer Spins |
Date & Time | Speaker | Title |
4/4 at 2pm | Vassily Gorbunov, U Aberdeen, Scotland | Hidden symmetries in equivariant cohomology related to quantum groups |
4/8 at 1pm | Jean-Bernard Zuber, U Pierre Marie Curie, Paris 6, France | Counting curves and knots and links |
Date & Time | Speaker | Title |
4/11 at 2pm | Jacopo Viti | Inhomogeneous quenches and arctic curves in fermionic systems. |
4/15 at 1pm | Vladimir Korepin | Statistical Mechanics and Combinatorics |
4/15 at 2pm | Tzu-Chieh Wei | Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods |
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Organized by: David Ben-Zvi, Roman Bezrukavnikov and Alexander Braverman
January 4-29th, 2016
The program will focus on emerging trends in representation theory and their relation to the more traditional ideas of the subject. The celebrated success of the perverse sheaves methods in 1980’s has led to development of a direction which may be called geometric categorification, where the primary object of study is a category of sheaves on an appropriate geometric space (stack): this includes theories of character sheaves, geometric Langlands duality, various approaches to categorification based on quiver varieties etc. Recently significant progress has been achieved in developing and systematizing these constructions and new algebraic methods inspired by D-modulesand perverse sheaves have been discovered. Other recent works indicate relation of this area to ideas of physical origin such as topological quantum field theory and wall-crossing, and their mathematical manifestations including cluster algebras, Bridgeland stabilities and quantum cohomology. The program will bring together experts in these different directions creating an opportunity for a synthesis of the diverse approaches and further progress.
All talks will be held in the SCGP Seminar Room, Rm 313.
Date | Time | Title | Speaker |
1/5/2016 | 10:30am | Loop Grassmannians, classifying spaces and local spaces | Ivan Mirkovic (U.Mass. Amherst) |
1/5/2016 | 2:30pm | Cohomological Hall algebras and affine quantum groups | Yaping Yang (U. Mass. Amherst) |
1/7/2016 | 10:30am | Elliptic quantum groups | Sachin Gautam (Perimeter Institute) |
1/7/2016 | 2:30pm | Recent Developments in the Geometric Langlands Program | Dima Arinkin (Wisconsin) |
1/11/2016 | 2:30pm | Elliptic stable envelopes | Andrei Okounkov (Columbia) |
1/12/2016 | 10:30am | Donaldson-Thomas transformations for moduli spaces of local systems on surfaces. | Alexander Goncharov (Yale) |
1/12/2016 | 2:30pm | Tilting modules and the p-canonical basis | Geordie Williamson (Max Planck) |
1/14/2016 | 10:30am | Semiclassical Geometric Langlands Correspondence | Dima Arinkin (Wisconsin) |
1/14/2016 | 2:30pm | Applications of 3d N=4 theories in geometric representation theory | Tudor Dimofte (Perimeter) |
1/15/2016 | 10:30am | BGG resolutions for rational Cherednik algebras | Stephen Griffeth (Talca) |
1/19/2016 | 10:30 am | Cherkis’ bow varieties and Coulomb branches of quiver gauge theories of affine type A. |
Hiraku Nakajima |
1/20/2016 | 10:30am | Studying the decomposition theorem over the integers | Geordie Williamson |
1/20/2016 | 2:30pm | Quivers and qq-characters
*Also part of the Seminar Series “Mathematics and Physics of Calogero-Moser-Sutherland systems” |
Nikita Nekrasov |
1/21/2016 | 10:30am | On categories O for quantized symplectic resolutions | Ivan Losev |
1/22/2016 | 10:30am | An involution based left ideal in the Hecke algebra | George Lusztig |
1/22/2016 | 10:30am | Miura bimodule, the affine Grassmannian, and nil-DAHA | Victor Ginzburg |
1/25/2016 | 10:30am | Towards a cluster structure on trigonometric zastava | Michael Finkelberg |
1/25/2016 | 2:30pm | Homomorphisms between different quantum toroidal and affine Yangian algebras. | Oleksandr Tsymbalyuk |
1/26/2015 | 10:30am | Microlocal Sheaves and Cluster Algebras | Harold Williams |
1/27/2015 | 10:30am | Perverse sheaves on arc spaces, central sheaves and local L-functions (joint work with D.Kazhdan and R.Bezrukavnikov). |
Alexander Braverman |
Organized by Simon Donaldson (SCGP), Hans-Joachim Hein (Maryland), Henry Guenancia (Stony Brook), Radu Laza (Stony Brook), Yuji Odaka (Kyoto), Song Sun (Stony Brook),Valentino Tosatti (Northwestern)
August 17-November 20th, 2015
Weekly Talks are held in SCGP Rm 313.
The theme of this program is the interaction between algebro-geometric and differential-geometric approaches. In algebraic geometry, one is interested in constructing compact moduli spaces of varieties. Even if one starts with manifolds, the compactification will almost always involve the inclusion of appropriate singular varieties. In a case when the manifolds have canonical metrics, such as Kahler-Einstein metrics, one can approach these questions differential-geometrically, studying the convergence of the metrics and the metric nature of the singular limits. Such ideas are well-established in the case of the moduli of curves and the Deligne-Mumford compactification. The purpose of this program is to make progress in higher dimensions, in the light of a number of recent developments coming from pluripotential theory, Riemannian convergence theory and algebraic geometry. The program will be an opportunity for specialists in the various different fields to interact and share expertise. Topics which will be discussed include:
1. The differential geometric interpretation of the moduli of varieties of general type constructed by Alexeev, Kollar, Shepherd-Barron.
2. Moduli spaces of Fano varieties, and connections with stability.
3. Kahler-Einstein metrics on singular varieties; their singularities and metric tangent cones.
4. Riemannian collapsing and large complex structure limits of Calabi-Yau manifolds.
Program Application is now closed.
Date | Time | Speaker | Title |
8/19 | 2:15 pm | Xiaowei Wang | GIT stability and compactification of moduli space |
8/21 | 2:15 pm | Jesus Martinez-Garcia | On the moduli space of cubic surfaces and their anticanonical divisors |
8/26 | 1:00 pm | Helge Ruddat | Mini-lectures on the Gross-Siebert program I: Introduction |
8/26 | 2:15 pm | Helge Ruddat | Mini-lectures on the Gross-Siebert program II: Toric degenerations, affine manifolds |
8/27 | 2:15 pm | Jian Song | Analytic base point free theorem |
8/28 | 2:15 pm | Helge Ruddat | Mini-lectures on the Gross-Siebert program III: Scattering and reconstruction of Calabi-Yau manifolds from degeneration data |
9/8 | 2:15 pm | Yuguang Zhang | Completion of the moduli space for polarized Calabi-Yau manifolds |
9/8 | 4:00 pm | Ben Weinkove | Complex surfaces and geometric flows |
9/9 | 1:00 pm | Chenyang Xu | Introduction of minimal model program and its applications |
9/9 | 2:15 pm | Chenyang Xu | Introduction of minimal model program and its applications |
9/11 | 2:15 pm | Cristiano Spotti | CscK resolutions of conically singular varieties: |
10/1 | 2:15 pm | Radu Laza | KSBA vs. GIT vs. Hodge theory |
10/12 | 2:15 pm | Paolo Cascini | Toroidal modifications. |
10/15 | 2:15 pm | Radu Laza | TBA |
10/22 | 2:15 pm | Ivan Cheltsov | Burkhardt, Todd, Igusa, Beauville and rational quartic threefolds |
10/27 | 2:15 pm | Sandor Kovacs | Projectivity of the moduli space of stable log-varieties |
10/29 | 2:30 pm | Martin de Borbon | Asymptotically Conical Ricci-Flat Kahler metrics with cone singularities |
11/3 | 2:30 pm | Tomoyuki Hisamoto | The strong version of K-stability derived from the coercivity property of the K-energy |
11/3 | 4:00 pm | Carl Tipler | From the Strominger system to generalized geometry |
11/5 | 2:30 pm | Yuji Sano | Minkowski problem on Fano polytopes |
11/16 | 12:30 pm | Mattias Jonsson | A variational approach to the Yau-Tian-Donaldson conjecture. (Part I) |
11/16 | 1:45 pm | Mattias Jonsson | A variational approach to the Yau-Tian-Donaldson conjecture. (Part II) |
11/17 | 2:30 pm | Henri Guenancia | Kähler-Einstein metrics on stable varieties |
Organized by Alexei Borodin,Peter Forrester, Yan Fyodorov, Alice Guionnet, Jon Keating, Mario Kieburg, and Jacobus Verbaarschot
August 24 – December 18, 2015
Weekly Talks are held in SCGP Room 313 at 11:00 am.
Random Matrix theory has been applied to many areas in pure and applied mathematics and in physics, ranging from correlations among the zeros of the Riemann function and the distribution of the longest increasing subsequences of permutations to the spacing distribution of nuclear levels and correlations of the eigenvalues of the Dirac operator in Quantum Chromo Dynamics. In this program we will discuss recent developments of random matrix theories beyond the ten fold classification in terms of large symmetric spaces. In particular we will focus on the following four areas: 1) Chiral random matrix theories with applications to gauge theories and the Riemann function. Nonperturbative properties of strongly interacting quantum held theories can be understood by means of random matrix theories with the same chiral symmetry breaking pattern. Recent work indicates that the same is true if the symmetries are softly broken by discretization effects or a chemical potential. Applications to the zeros of the Riemann function, Dirac spectra in lower dimensions and relations with topological insulators will be discussed as well. 2) The relation between integrability and random matrix theory. Invariant random matrix theories can be solved because of underlying integrable structures such as for example the Toda lattice equation. More complicated ensembles still can be solved suggesting that an underlying integrable structure exists and we hope to explore such relations in this program. 3) Universal properties on non-invariant random matrix ensembles. Examples are Wigner matrices, ensembles of sparse matrices and band matrices. In particular, band matrices describe the transition between Poisson and Wigner-Dyson eigenvalue statistics and have been used to study scaling properties of localization. Based on recent work showing that these properties are universal we hope to make further progress in this area. 4) Random Matrix Theory and dynamics. This goes back as far as Dyson Brownian motion model for the eigenvalues of random matrices, but recently this topic received a great deal of attention in the context of non-equilibrium dynamics and the Kardar-Parisi-Zhang equation. This is also the topic of the workshop Random matrices, random growth processes and statistical physics from September 6-11 which is part of this program. Related issues such as the Langevin evolution of random matrix spectra and relations between the stochastic Loewner equation and random matrix theory will be discussed as well. A second workshop related to physics applications of random matrix theory may be organized later in the program.
Program application is now closed.
Date | Speaker | Title |
8/28 | Peter Forrester | Raney distribution and random matrices |
9/14 | Shinsuke Nishigaki, Shimane University, Japan | Tracy-Widom distribution and spontaneous SUSY breaking in a matrix model of 2D IIA superstrings |
9/16 | Arno Kuijlaars, Universiteit van Leuven, Belgium | Products of random matrices |
9/18 | Pierre van Moebeke University of Louvain, Belgium | The Tacnode GUE-Minor Process |
9/30 | Mariya Shcherbina, Institute for Low Temperature Physics, National Ac. Sci. of Ukraine |
Central limit theorem for linear eigenvalue statistics of random matrices with independent or weakly dependent entries. |
10/1 | Hans Weidenmueller, Max Planck Institut for Kernphysik, Heidelberg | Neutron Resonance Widths and the Porter-Thomas Distribution |
10/5 | Tilo Wettig, University of Regensburg | On Zirnbauer’s approach to induced QCD |
10/7 | Mark Adler, Brandeis University | Double Aztec Diamonds and Lozenge Tilings with Irregular Boundaries |
10/9 | Gernot Akemann, Bielefeld University | Recent progress in products of random matrices |
10/12 | Francesco Mezzadri (Bristol University) | Global Fluctuations of Linear Statistics of beta Ensembles |
10/14 | Nina Snaith (Bristol University) | Combining random matrix theory and number theory |
10/16 | Tatyana Shcherbina (St. Petersburg State University) | Random band matrices: delocalization and universality |
10/23 | Thomas Seligman, UNAM Mexico and CIC Cuernavaca | Random matrix ensembles of density matrices from first principles and from random matrix dynamics. [1] |
10/28 | Manan Vyas | Random Matrix Theory for Quantum Many-body systems |
10/30 | Fabio Franchini, ICTP Trieste | Ergodicity breaking in invariant matrix models |
11/9 | Mario Kieburg, University of Duisburg-Essen | Products of Random Matrices and Quantum Information Theory |
11/11 | Pjotr Warchot, Jagiellonian University, Cracow | Correlators of left and right eigenvectors of non-Hermitian random matrices. |
11/13 | James Osborn, Argonne National Laboratory | Lattice Dirac Fermions and Chiral Effective Theories |
11/18 | Miguel Tierz, University of Madrid | Matrix models in Chern-Simons-matter theory |
11/20 | Nivedita Deo, University of Delhi | Counting RNA Folds From Random Matrix Models And Networks |
Abstract: Calogero-Moser-Sutherland many-body systems arose originally in the 1970’s simultaneously in Nuclear Physics, Mathematical Physics and Solid State Physics. Since then they were found in some incarnations in diverse branches of physics and mathematics such as the theory of quantum Hall effect, Yang-Mills and Chern-Simons gauge theories in various dimensions with various amounts of supersymmetry, noncommutative geometry, topology of Hilbert schemes, geometric representation theory, Gromov-Witten invariants, theory of symmetric functions, SLE, Random Matrix theory, collective field theory and random geometries.
The aim of the seminar series is to review and explore these connections.
The weekly talks take place on Wednesdays at 2:30pm (beginning Wednesday April 15) in room 313.
VideosDate and Time | Title | Presenters | Video |
4/15 at 2:30pm – Room 313 | Mathematics and Physics of Calogero Moser-Sutherland systems | Nikita Nekrasov | Video |
4/22 at 2:30pm – Room 313 | Quantum Integrability and Schubert Calculus | Vassily Gorbounov | Video |
4/29 at 2:00pm – Room 313 | From crossed instantons to Calogero-Moser system | Nikita Nekrasov | |
5/6 at 2:30pm – Room 313 | |||
5/13 at 2:30pm – Room 313 |
Organized by John Morgan and Dennis Sullivan
October 1, 2014 – June 30, 2015
While activities will depend on the visitors for their specific focus, we expect them to be organized around several general themes: (i) rigorous approaches to perturbative quantum field theories, and especially to gauge theories using homological and homotopy-theoretic techniques, (ii) formal quantization, and (iii) TQFTs and infinity structures. Within those themes, a partial list of topics would include: BV algebras; operads; the Fukaya category; various compactifications of moduli spaces of stable curves and stable maps, as in string topology and contact homology and twisted K-theory. Our plan is to have activity spread over the entire academic year, rather than a more concentrated activity during one semester, with between 4 and 6 visitors in residence at any one time. In addition to Fukaya, Sullivan, and Morgan, who are permanently in residence at Stony Brook, those who have expressed interest in attending the program (for 3 weeks to a month, with a few longer visits) include Kevin Costello, Jacob Lurie, Dan Freed, Constantin Teleman, and Alberto Cattaneo.
Application for program is now closed.
As part of the Simons Center program, Interactions of Homotopy Theory and Algebraic Topology with Physics through Algebra and Geometry, John Morgan will give a series of lectures (8 to 10 lectures) on Sheaf Theory with applications to duality. The course will be aimed at intermediate graduate students and above. The only prerequisite is a basic course in algebraic topology.
These lectures will be on Fridays at 2:45pm, in the Simons Center seminar room, 313 beginning Friday October 3.
Title: A Topologist looks at Sheaf Theory
Abstract:
Sheaf theory has long been an essential tool in algebraic geometry, algebraic number theory, and complex analysis, but its inspiration comes directly from topology. This lecture course will emphasize these roots, hopefully making sheaf theory seem natural to those with a topological bent. The course will begin by covering the basic topics in sheaf theory describing the objects and the four basic maps of the theory and then will culminate with a discussion of Verdier duality, which generalizes Poincare duality.
This theory will then be applied to define a bordism theory, called duality bordism, whose coefficient group agrees with the Grothendieck group of chain complexes satisfying Poincare duality modulo those that sit as the boundary term in an exact sequence satisfying Lefschetz duality. This bordism group is the Pontryjagin dual homology theory to the cohomology theory associated with surgery theory. This means that a surgery problem is completely classified by evaluating surgery obstructions (signatures, and Arf invariants) of its restrictions to all possible duality bordism elements.
Direct analysis of this bordism theory allows one to identify it at odd primes with real K-theory and at the prime 2 with ordinary homology.
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