CMSA

A Mean Field View of the Landscape of Two-Layers Neural Networks
2018-03-28 16:30 - 17:30 (America/New_York) | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Andrea Montanari (Stanford)
Title: A Mean Field View of the Landscape of Two-Layers Neural Networks
Abstract: Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD). Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties? We consider a simple case, namely two-layers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to ‘average-out’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well. [Based on joint work with Song Mei and Phan-Minh Nguyen]

4-2-2018 Mathematical Physics Seminar
2018-04-02 12:00 - 13:30 | MA

Math Science Lectures in Honor of Raoul Bott, April 2-3
2018-04-02 16:30 - 2018-04-03 18:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On April 2-3, the CMSA will be hosting two lectures by Freddy Cachazo (Perimeter Institute) on “Geometry and Combinatorics in Particle Interactions.” This will be the first of the new annual Bott Math Science Lecture Series hosted by the CMSA.
The lectures will take place from 4:30-5:30pm in Science Center, Hall D.

Black Holes and Naked Singularities
2018-04-04 16:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Ramesh Narayan, Department of Astronomy, Harvard University
Title: Black Holes and Naked Singularities
Abstract: Black Hole solutions in General Relativity contain Event Horizons and Singularities. Astrophysicists have discovered two populations of black hole candidates in the Universe: stellar-mass objects with masses in the range 5 to 30 solar masses, and supermassive objects with masses in the range million to several billion solar masses. There is considerable evidence that these objects have Event Horizons. It thus appears that astronomical black hole candidates are true Black Holes. Direct evidence for Singularities is much harder to obtain since, at least in the case of Black Holes, the Singularities are hidden inside the Event Horizon. However, General Relativity also permits Naked Singularities which are visible to external observers. Toy Naked Singularity models have been constructed, and some observational features of accretion flows in these spacetimes have been worked out.

Simons Collaboration Workshop, April 5-7, 2018
2018-04-05 09:00 - 2018-04-07 17:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
The CMSA will be hosting a three-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 5-7, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.
Please click here to register for this event. We have space for up to 30 registrants on a first come, first serve basis.
We may be able to provide some financial support for grad students and postdocs interested in this event. If you are interested in funding, please send a letter of support from your mentor to Hansol Hong.
Confirmed Speakers:

Jacob Bourjaily (Niels Bohr Institute)
Mandy Cheung (Havard University)
Tristan Collins (Harvard University)
Yoosik Kim (Boston University)
Yu-Shen Lin (Harvard University)
Cheuk-Yu Mak (Cambridge University)
Yu Pan (MIT)
Mauricio Romo (Tsinghua University)
Shu-Heng Shao (IAS)
Zack Sylvan (Columbia University)
Dmitry Vaintrob (IAS)

Workshop on Coding and Information Theory
2018-04-09 09:00 - 2018-04-13 15:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
The workshop on coding and information theory will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.
This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.
Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory. One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program. Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities. Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics. All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.
Participation: The workshop is open to participation by all interested researchers, subject to capacity.
A list of lodging options convenient to the Center can also be found on our recommended lodgings page.
Confirmed participants include:

Emmanuel Abbe, Princeton University
Simeon Ball, Universitat Politècnica de Catalunya
Boris Bukh, Carnegie Mellon University
Mahdi Cheraghchi, Imperial College London
Sivakanth Gopi, Princeton University
Elena Grigorescu, University of Purdue
Hamed Hassani, University of Pennsylvania
Navin Kashyap, Indian Institute of Science
Young-Han Kim, University of California, San Diego
Swastik Kopparty, Rutgers University
Nati Linial, Hebrew University of Jerusalem
Shachar Lovett, University of California, San Diego
William Martin, Worcester Polytechnic Institute
Arya Mazumdar, University of Massachusetts at Amherst
Or Meir, University of Haifa
Olgica Milenkovic, ECE Illinois
Chandra Nair, Chinese University of Hong Kong
Yuval Peres, Microsoft Research
Yury Polyanskiy, Massachusetts Institute of Technology
Maxim Raginsky, University of Illinois at Urbana-Champaign
Sankeerth Rao Karingula, UC San Diego
Ankit Singh Rawat, MIT
Noga Ron-Zewi, University of Haifa
Ron Roth, Israel Institute of Technology
Atri Rudra, State University of New York, Buffalo
Alex Samorodnitsky, Hebrew University of Jerusalem
Itzhak Tamo, Tel Aviv University
Amnon Ta-Shma, Tel Aviv University
Himanshu Tyagi, Indian Institute of Science
David Zuckerman, University of Texas at Austin

4-9-2018 Math Physics Seminar
2018-04-09 12:00 | MA

Graph Structure in Polynomial Systems: Chordal Networks
2018-04-11 16:30 - 17:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Pablo Parillo (MIT)
Title: Graph Structure in Polynomial Systems: Chordal Networks
Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).

4-13-2018 Mirror Symmetry Seminar
2018-04-13 11:00 - 12:00 | MA

On the fibration structure of known Calabi-Yau threefolds
2018-04-13 16:30 - 17:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Washington Tayor (MIT)
Title: On the fibration structure of known Calabi-Yau threefolds
Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds.

4-16-2018 Mathematical Physics Seminar
2018-04-16 12:00 | MA

4-16-2018 Social Science Applications Forum
2018-04-16 17:16 | MA

4-17-2018 Special Algebraic Geometry Seminar
2018-04-17 12:00 - 13:30 | MA

4-20-2018 Social Science Applications Forum
2018-04-20 17:18 | MA

4-23-2018 Math Physics
2018-04-23 17:15 | MA

4/30/2018 Special Seminar
2018-04-30 13:30 - 14:30 | MA

From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
2018-08-18 08:30 - 2018-08-20 17:20 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
On August 18 and 20, 2018, the Center of Mathematic Sciences and Applications and the Harvard University Mathematics Department hosted a conference on From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford. The talks took place in Science Center, Hall B.
Saturday, August 18th: A day of talks on Vision, AI and brain sciences
Monday, August 20th: a day of talks on Math
Speakers:

Stuart Geman, Brown
Janos Kollar, Princeton
Tai Sing Lee, CMU
Emanuele Macri, Northeastern
Jitendra Malik, Berkeley / FAIR
Peter Michor, University of Vienna
Michael Miller, Johns Hopkins
Aaron Pixton, MIT
Jayant Shah, Northeastern
Josh Tenenbaum, MIT
Burt Totaro, UCLA
Avi Wigderson, IAS
Ying Nian Wu, UCLA
Laurent Younes, Johns Hopkins
Song-Chun Zhu, UCLA

Organizers:

Ching-Li Chai, University of Pennsylvania
David Gu, Stony Brook University
Amnon Neeman, Australian National University
Mark Nitzberg, University of California at Berkeley
Yang Wang, Hong Kong University of Science and Technology
Shing-Tung Yau, Harvard University
Song-Chun Zhu, University of California, Los Angeles

Publication:
Pure and Applied Mathematics Quarterly
Special Issue: In Honor of David Mumford
Guest Editors: Ching-Li Chai, Amnon Neeman

Big Data Conference 2018
2018-08-23 08:30 - 2018-08-24 16:30 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On August 23-24, 2018 the CMSA hosted the fourth annual Conference on Big Data. The Conference featured speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.
The talks were held in Science Center Hall B, 1 Oxford Street.
Speakers:

Mohammad Akbarpour, Stanford
Emily Breza, Harvard
Francesca Dominici, Harvard
Chiara Farronato, Harvard
Kobi Gal, Ben Gurion
Jonah Kallenbach, Reverie Labs
Samuel Kou, Harvard
Laura Kreidberg, Harvard
Danielle Li, MIT
Libby Mishkin, Uber
Josh Speagle, Harvard
William Stein, University of Washington
Alex Teyltelboym, University of Oxford
Sergiy Verstyuk, CMSA/Harvard

Organizers:

Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
Richard Freeman, Herbert Ascherman Professor of Economics, Harvard University
Jun Liu, Professor of Statistics, Harvard University
Horng-Tzer Yau, Professor of Mathematics, Harvard University

PROGRAM ON TOPOLOGICAL ASPECTS OF CONDENSED MATTER
2018-08-27 09:00 - 2019-05-05 17:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
During Academic year 2018-19, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines.
As part of the Program, the CMSA will be hosting two workshops:

Workshop on Topology and Quantum Phases of Matter (August 27-28, 2018)
Workshop on Topological Aspects of Condensed Matter (September 10-11, 2019)

.
Additionally, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program

Name
Tentative Visiting Dates

Jason Alicea

11/12/2018-11/16/2018

Maissam Barkeshli
4/22/2019 – 4/26/2019

Xie Chen
4/15-17/2019 4/19-21/2019 4/24-30/2019

Lukasz Fidkowski

1/7/2019-1/11/2019

Zhengcheng Gu

8/15/2018-8/30/2018 & 5/9/2019-5/19/2019

Yin Chen He

10/14/2018-10/27/2018

Anton Kapustin
8/26/2018-8/30/2018 & 3/28/2019-4/5/2019

Michael Levin

3/11/2019-3/15/2019

Yuan-Ming Lu
4/29/2019-6/01/2019

Adam Nahum

4/2/2019- 4/19/2019

Masaki Oshikawa

4/22/2019-5/22/2019

Chong Wang
10/22/2018-11/16/2018

Juven Wang

4/1/2019-4/16/2019

Cenke Xu
8/26/2018-10/1/2018

Yi-Zhuang You

4/1/2019-4/19/2019

Mike Zaletel

5/1/2019-5/10/2019

Kickoff Workshop on Topology and Quantum Phases of Matter
2018-08-27 09:20 - 2018-08-28 15:15 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
On August 27-28, 2018, the CMSA will be hosting a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines.
This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter, and will be the first of two workshops, in addition to a visitor program and seminars.
The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.
Speakers:

Zhen Bi, MIT
Meng Cheng, Yale
Dima Feldman, Brown
Dominic Else, UCSB
Liang Fu, MIT
Fabian Grusdt, Harvard
Ying Fei Gu, Harvard
Bert Halperin, Harvard
Anton Kapustin, Caltech
Patrick Lee, MIT
L. Mahadevan, Harvard
Brad Marston, Brown
Max Metlitski, MIT
Emil V. Prodan, Yeshiva
Achim Rosch, University of Cologne
Mathias Scheurer, Harvard
Marin Soljacic, MIT
X. G. Wen, MIT
Cenke Xu, UCSB
Frank Zhang, Cornell

Topological Aspects of Condensed Matter Seminar
2018-08-29 17:36 | MA
As part of the Program on Topological Aspects of Condensed Matter, a weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

Date
Speaker
Title/Abstract

8/29/2018
Zeng-Cheng Gu
Title: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory
Abstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.

9/10/2018
Dominic Else, MIT
Video
Title: Phases and topology in periodically driven (Floquet) systems
Abstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.

9/17/2018
Adrian Po, MIT
Video
Title: A modern solution to the old problem of symmetries in band theory
Abstract: There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants.

9/24/2018
Maxim Metlitski
Title: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs
Abstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.

10/1/2018
Cancelled

10/9/2018
Tuesday
3:00-4:30pm
Sagar Vijay
Title: Fracton Phases of Matter
Abstract: Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped, point-like excitations (“fractons”) that are strictly immobile at zero temperature, and by degenerate ground-states that are locally indistinguishable. Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions, and these states of matter are a gateway for exploring mechanisms for quantum information storage, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases, constructions of these states using well-studied two-dimensional topological phases, and a model in which the fracton excitations carry a protected internal degeneracy, which provides a natural generalization of non-Abelian anyons to three spatial dimensions. I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.

10/15/2018
Ethan Lake
Title: A primer on higher symmetries
Abstract: The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.

10/22/2018
Room G02
Yin-Chen He, Perimeter
Title: Emergent QED3 and QCD3 in condensed matter system
Abstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.

10/29/2018
Dominic Williamson, Yale
Video
Title: Symmetry and topological order in tensor networks
Abstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.

11/13/2018
Tuesday
3:00-4:30pm
Jason Alicea, Caltech
Title: Time-crystalline topological superconductors

11/19/2018
X. G. Wen, MIT
Video
Title: A classification of 3+1D topological orders
Abstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.

12/3/2018
*Room G02*
Claudio Chamon, Boston University
Title: Many-body scar states with topological properties in 1D, 2D, and 3D.
Abstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies.

12/10/2018
Room G02
Anders Sandvik, Boston University and Institute of Physics, CAS, Beijing
Title: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets
Abstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.

1/8/2019
Lukasz Fidkowski, Univ. of Washington
Video
Title: Non-trivial quantum cellular automata in 3 dimensions
Abstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom. This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.

3/18/2019
Ari Turner, Technion
Video
Title: Trapping Excitations at Phantasmagoric Wave Vectors
Abstract: This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this, and also introduce “finite fields”, which are the number systems one needs to define exponentials mod. 2.

4/1/2019
Yi-Zhuang You (UCSD)
Title: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points
Abstract: Noether’s theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s theorem at the deconfined quantum critical point (DQCP), which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.

4/8/2019
Adam Nahum (Oxford)
Title: Emergent statistical mechanics of entanglement in random unitary circuits
Abstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.

4/16/2019
Lyman 425
1:30pm
Xie Chen (Calthech)
Title: Foliated Fracton Order
Abstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk, I will present a new framework, which we call the “foliated fracton order”, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models, but also points to the direction of search for interesting new features.

4/24/2019
10:30am
Michael Freedman (Microsoft Station Q)
Video
Title: Quantum cellular automata in higher dimensions
Abstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.

4/26/2019
10:30am
Maissam Barkeshli (University of Maryland)
Video
Title: Relative anomalies in (2+1)D symmetry enriched topological states
Abstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.

5/3/2019
Yuan-Ming Lu (Ohio State)
Title: Spontaneous symmetry breaking from anyon condensation
Abstract: In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

5/9/2019
10:30am
Michael Zaletel (UC Berkeley)
Title: Three-partite entanglement in CFTs and chiral topological orders
Abstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement, multi-partite entanglement is far richer, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure, the “entanglement of purification,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders, and solicit the audience’s help in proving or disproving it.

5/28/2019
10:30am
Masaki Oshikawa (U Tokyo)
Title: Gauge invariance, polarization, and conductivity

Abstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors, and also to general constraints on the electric conductivity.

7/18/2019
Eslam Khalaf (Harvard)

Title: Dynamical correlations in anomalous disordered wires

Abstract: In a (multichannel) disordered wire, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case, the classical dynamics are described by diffusion + drift, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.

The problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.

The mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.

9/10/18 Topology Seminar
2018-09-10 10:30 - 12:00 | MA

9/10/2018 Math-Physics Seminar
2018-09-10 17:41 | MA

9/12/2018 GR Seminar
2018-09-12 17:52 | MA

9/17/2018 Math-Physics Seminar
2018-09-17 17:53 | MA

9/24/2018 Math-Physics Seminar
2018-09-24 17:55 | MA

9/24/2018 Topological Aspects of Condensed Matter Seminar
2018-09-24 17:56 | MA

GR Seminar 9/26/2018
2018-09-26 17:59 | MA

F-Theory Workshop
2018-09-29 08:30 - 2018-09-30 15:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
The CMSA hosted an F-Theory workshop September 29-30, 2018. The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.
Youtube Playlist
Organizers:

Paolo Aluffi (Florida State)
Lara B. Anderson (Virginia Tech)
Mboyo Esole (Northeastern)
Shing-Tung Yau (Harvard)

Speakers:

Mirjam Cvetic, University of Pennsylvania
Tommaso de Fernex, University of Utah
James Gray, Virginia Tech
Jonathan Heckman, University of Pennsylvania
Monica Kang, Harvard University
Sándor Kovács, University of Washington
Anatoly Libgober, UIC
Matilde Marcolli, Caltech, University of Toronto, and Perimeter Institute
Washington Taylor, MIT
Cumrun Vafa, Harvard University

10/01/2018 Math-Physics Seminar
2018-10-01 18:01 | MA
