Machine Learning Physics: From Quantum Mechanics to Holographic Geometry
2019-04-17 16:30 - 17:30 (America/New_York) | MA
Speaker: Yi–Zhuang You (UCSD)

Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

[1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103
[2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804
[3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223

Yip Annual Lecture
2019-04-18 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On April 18, 2019 Harvard CMSA hosted the inaugural Yip lecture. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Peter Galison (Harvard Physics).
The lecture was held from 4:00-5:00pm in Science Center, Hall A.

4/18/2019 General Relativity Seminar
2019-04-19 09:30 - 10:30 | MA

4/22/2019 Quantum Matter Seminar
2019-04-22 10:30 - 12:00 | MA

4/22/2019 Math Physics Seminar
2019-04-22 12:00 - 13:00 | MA

4/24/2019 Topological Aspects of Condensed Matter Seminar
2019-04-24 10:30 - 12:00 | MA

4/24/2019 General Relativity Seminar
2019-04-24 10:30 - 23:30 | MA

4/24/2019 Fluid Dynamics Seminar
2019-04-24 15:00 - 16:00 | MA

Credible Mechanisms
2019-04-24 16:30 - 17:30 | MA
Speaker: Shengwu Li (Harvard)

Title: Credible Mechanisms

Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.

4/25/2019 Fluid Dynamics Seminar
2019-04-25 00:00 - 13:00 | MA

4/25/2019 General Relativity Seminar
2019-04-25 10:30 - 23:30 | MA

4/26/2019 Topology
2019-04-26 10:30 - 12:40 | MA

4/26/2019 General Relativity Seminar
2019-04-26 14:30 - 2020-04-26 15:30 | MA

Conference on Algebraic Geometry, Representation theory and Mathematical Physics
2019-04-29 09:00 - 2019-05-01 17:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
From April 29 to May 1, 2019 the CMSA will be hosting a Conference on Algebraic Geometry, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.
Videos
Speakers:

Dan Abramovich, Brown
Roman Bezrukavnikov, MIT
Fedor Bogomolov, NYU
Qile Chen, Boston College
Dawei Chen, Boston College
Alexander Efimov, Moscow
Pavel Etingof, MIT
Maksym Fedorchuk, Boston College
Dennis Gaitsgory, Harvard
Amin Gholampour, Maryland
Brendan Hassett, Brown
Ludmil Katzarkov, Miami & Moscow
Si Li, Tsinghua
Andrei Negut, MIT
Yuri Tschinkel, NYU
Wei Zhang, MIT

Monday, April 29

Time
Speaker
Title/Abstract

8:30 – 9:00am
Breakfast

9:00 – 10:00am
Wei Zhang, MIT
Title: The arithmetic fundamental lemma for diagonal cycles
Abstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization, the arithmetic Gan-Gross-Prasad conjecture, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions. The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.

10:00 – 10:30am
Break

10:30 – 11:30am
Yuri Tschinkel, NYU
Title: Equivariant birational geometry and modular symbols
Abstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).

11:30 – 1:30pm
Lunch

1:30 – 2:30pm
Alexander Efimov, Moscow
Title: Torsionness for regulators of canonical extensions
Abstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.

2:30 – 3:00pm
Break

3:00 – 4:00pm
Amin Gholampour, Maryland
Title: Euler Characteristics of punctual quot schemes on threefolds
Abstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F, n) and Quot(G,n), where Quot(-,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.

4:00 – 4:30pm
Break

4:30 – 5:30pm
Maksym Fedorchuck, BC
Title: Stability of one-parameter families of weighted hypersurfaces
Abstract: We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space. The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions, and, if time permits, examples where this machinery can be used to produce birational models with good properties. Joint work with Hamid Ahmadinezhad and Igor Krylov.

Tuesday, April 30

Time
Speaker
Title/Abstract

8:30 – 9:00am
Breakfast

9:00 – 10:00am
Brendan Hassett, Brown
Title: Rationality for geometrically rational threefolds
Abstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure, like smooth complete intersections of two quadrics. (joint with Tschinkel)

10:00 – 10:30am
Break

10:30 – 11:30am
Dennis Gaitsgory, Harvard
Title: The Fundamental Local Equivalence in quantum geometric Langlands
Abstract: The Fundamental Local Equivalence is statement that relates the q-twisted Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its dual is combinatorial, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra, which in itself is a geometric device that concisely encodes the root data.

11:30 – 1:00pm
Lunch

1:00- 2:00pm
Andrei Negut, MIT
Title: AGT relations in geometric representation theory
Abstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces, and the goal is to connect them with the W-algebra of type gl_n.

2:00 – 2:15pm
Break

2:15 – 3:15pm
Dan Abramovich, Brown
Title: Resolution in characteristic 0 using weighted blowing up
Abstract: Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved.
Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop.
We show that there is a functorial way to resolve varieties using emph{weighted} blowings up, in the stack-theoretic sense. To an embedded variety $X subset Y$ one functorially assigns an invariant $(a_1,ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.
This is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.

3:15 – 3:30pm
Break

3:30 – 4:30pm
Fedor Bogomolov, NYU
Title: On the base of a Lagrangian fibration for a compact hyperkahler manifold.
Abstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.

4:30 – 4:45pm
Break

4:45 – 5:45pm
Dawei Chen, BC
Title: Volumes and intersection theory on moduli spaces of Abelian differentials
Abstract: Computing volumes of moduli spaces has significance in many fields. For instance, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

Wednesday, May 1

Time
Speaker
Title/Abstract

8:30 – 9:00am
Breakfast

9:00 – 10:00am
Pavel Etingof, MIT
Title: Short star-products for filtered quantizations
This is joint work with Eric Rains and Douglas Stryker.

10:00 – 10:30am
Break

10:30 – 11:30am
Roman Bezrukavnikov, MIT
Title: Stability conditions and representation theory
Abstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)
and its relation to modular Lie algebra representations. I will also address a potential generalization of that picture
to modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.

11:30 – 11:45am
Break

11:45 – 12:45pm
Qile Chen, BC
Title: Counting curves in critical locus via logarithmic compactification
Abstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles, the non-compactness of the R-maps moduli makes such powerful torus action useless.
In this talk, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action.
This is a joint work with Felix Janda and Yongbin Ruan.

12:45 – 2:30pm
Lunch

2:30 – 3:30pm
Si Li, Tsinghua
Title: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry
Abstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.

3:30 – 4:00pm
Break

4:00 – 5:00pm
Ludmil Katzarkov, Moscow
Title: PDE’s non commutative motives and HMS.
Abstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir. Geometry will be discussed.

4/29/2019 Quantum Matter seminar
2019-04-29 10:30 - 12:00 | MA

4/29/2019 Mathematical Physics Seminar
2019-04-29 12:00 - 13:00 | MA

5/1/2019 Fluid Dynamics Seminar
2019-05-01 15:00 - 16:00 | MA

Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
2019-05-02 09:00 - 2019-05-05 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On May 2-5, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the Science Center, Lecture Hall C.
Organizers:

Horng-Tzer Yau (Harvard)
Wilfried Schmid (Harvard)
Clifford Taubes (Harvard)
Cumrun Vafa (Harvard)

Speakers:

Lydia Bieri, University of Michigan
Tristan Collins, MIT
Simon Donaldson, Imperial College
Fan Chung Graham, UC San Diego
Nigel Hitchin, Oxford University
Jun Li, Stanford University
Kefeng Liu, UCLA
Chiu-Chu Melissa Liu, Columbia University
Alina Marian, Northeastern University
Xenia de la Ossa, Oxford University
Duong H. Phong, Columbia University
Richard Schoen, UC Irvine
Andrew Strominger, Harvard University
Nike Sun, MIT
Clifford Taubes, Harvard University
Chuu-Lian Terng, UC Irvine
Valentino Tosatti, Northwestern University
Karen Uhlenbeck, University of Texas
Cumrun Vafa, Harvard University
Mu Tao Wang, Columbia University
Edward Witten, IAS
Stephen Yau, Tsinghua University, P.R. China

5/6/2019 Math Physics
2019-05-06 12:00 - 13:00 | MA

5/15/2019 Fluid Dynamics
2019-05-15 15:00 - 16:00 | MA

5/22/2019 Fluid Dynamics Seminar
2019-05-22 15:00 - 16:00 | MA

5/28/2019 Topological Aspects of Condensed Matter Special Seminar
2019-05-28 10:30 - 11:42 | MA

2019 Big Data Conference
2019-08-19 08:30 - 2019-08-20 16:40 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
On August 19-20, 2019 the CMSA hosted the fifth annual Conference on Big Data. The Conference will featured many 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 will take place in Science Center Hall D, 1 Oxford Street.
Videos can be found in the Youtube playlist.

Workshop on Foundations of Computational Science
2019-08-29 08:30 - 2019-08-31 14:45 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
On August 29-31, 2019 the Center of Mathematical Sciences and Applications hosted a workshop on Foundations of Computational Science. The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop was organized by David Xianfeng Gu.
Speakers:

Sarah Adel Bargal, Boston University
Jianfeng Chen, Harvard
Tat Seng Chua, National University of Singapore
Ke Deng, Tsinghua
David Xianfeng Gu, Stony Brook
Yike Guo, Imperial College London
Minlie Huang, Tsinghua
Scott Kominers, Harvard
Brian Kulis, Boston University
Wee Sun Lee, National University of Singapore
Qianxiao Li, National University of Singapore
Hanzhong Liu, Tsinghua
Jun Liu, Harvard
Xiao-Li Meng, Harvard
Cengiz Pehlevan, Harvard
Donald Rubin, Harvard
Suproteem Sarkar, Harvard
Zuowei Shen, National University of Singapore
Yuanchun Shi, Tsinghua
Justin Solomon, MIT
Hang Su, Tsinghua
Maosong Sun, Tsinghua
Mirac Suzgun, Harvard
Sergiy Verstyuk, CMSA
Xiaoqin Wang, Tsinghua
Bin Xu, Tsinghua
Jun Zhu, Tsinghua
Wenwu Zhu, Tsinghua

Spacetime and quantum mechanics, total positivity and motives
2019-09-01 09:00 - 2019-12-20 17:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Recent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during Fall 2019, with between 20-30 participants. They will also invite 10-20 longer-term visitors throughout the semester. Additionally, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10.
Organizers:

Nima Arkani-Hamed (IAS)
Lauren Williams (Harvard)
Alexander Postnikov (MIT)
Thomas Lam (Michigan)

.
Workshops:

Spacetime and Quantum Mechanics Workshop, October 28-30, 2019

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

Paolo Benincasa, 11/17/2019 – 11/29/2019
Jacob Bourjaily, 9/1/2019 – 12/15/2019
Francis Brown, 9/15/2019 – 9/20/2019
Simon Caron-Huot, 9/30/2019 – 10/04/2019
Lance Dixon, 9/9/2019 – 9/20/2019
Charles Doran, 10/19/2019 – 11/1/2019
James Drummond, 10/14/2019 – 10/18/2019
Nick Early, 11/18/2019 – 11/22/2019
Livia Ferro, 10/27/2019 – 11/9/2019
Sergey Fomin, 10/6/2019 – 10/16/2019
Sebastian Franco, 10/9/2019 – 10/19/2019
Hadleigh Frost, 9/15/2019 – 12/20/2019
Michael Green, 10/05/2019 – 10/13/2019
Alexander Goncharov, 12/05/2019 – 12/20/2019
Song He, 9/29/2019 – 11/10/2019
Xuhua He, 10/30/2019-11/03/2019
Enrico Herrmann, 10/27/2019 – 11/9/2019
Yutin Huang, 9/30/2019 – 10/12/2019
Steven Karp, 10/11/2019 – 11/03/2019
Tomasz Lukowski, 10/27/2019 – 11/11/2019
Andrew McLeod, 10/6/2019 – 10/19/2019 & 11/3/2019 – 11/16/2019
Sebastian Mizera, 10/28/2019 – 11/1/2019
Erik Panzer, 9/15/2019 – 9/25/2019
Matteo Parisi, 10/26/2019 – 11/10/2019
Julio Parra-Martinez, 10/10/2019 – 05/12/2019
Pierpaolo Mastrolia, 11/8/2019 – 11/16/2019
Pasha Pylyavskyy, 9/8/2019 – 9/22/2019 & 10/14/2019 – 11/1/2019
Junjie Rao, 10/25/2019 – 11/04/2019
Giulio Salvatori, 9/3/2019 – 12/15/2019
Michael Shapiro, 10/27/2019 – 11/2/2019
David Speyer, 10/14/2019 – 10/18/2019
Hugh Thomas, 10/27/2019 – 11/22/2019
Jaroslav Trnka, 9/30/2019 – 10/04/2019, 10/28/2019 – 11/01/2019, 11/18/2019 – 11/22/2019
Cristian Vergu, 11/10/2019 – 11/30/2019
Matthias Volk, 10/14/2019 – 10/25/2019
Matthew von Hippel, 11/11/2019 – 11/22/2019
Pierre Vanhove, 10/22/2019 – 10/31/2019
Matthias Wilhelm, 10/14/2019 – 10/25/2019

9/9/2019 Math-Physics Seminar
2019-09-09 12:00 - 13:00 | MA

Topology and Dynamics in Quantum Matter Workshop
2019-09-10 09:15 - 2019-09-11 15:25 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
On September 10-11, 2019, the CMSA hosted a second workshop on Topological Aspects of Condensed Matter.
New ideas rooted in topology have recently had a major impact on condensed matter physics, and have led to new connections with high energy physics, mathematics and quantum information theory. The aim of this program will be to deepen these connections and spark new progress by fostering discussion and new collaborations within and across disciplines.
Topics include i) the classification of topological states ii) topological orders in two and three dimensions including quantum spin liquids, quantum Hall states and fracton phases and iii) interplay of symmetry and topology in quantum many body systems, including symmetry protected topological phases, symmetry fractionalization and anomalies iv) topological phenomena in quantum systems driven far from equlibrium v) quantum field theory approaches to topological matter.
This workshop is part of the CMSA’s program on Program on Topological Aspects of Condensed Matter, and is the second of two workshops, in addition to a visitor program and seminars.
The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.
Organizers: Michael Hermele (CU Boulder) and Ashvin Vishwanath (Harvard)
Partial list of speakers:

Nima Arkani-Hamed, IAS
Jennifer Cano, Stony Brook
Meng Cheng, Yale
Lukasz Fidkowski, UW Seattle
Daniel Freed, Texas
Jeongwan Haah, Microsoft Research
Anton Kapustin, Caltech
Zohar Komargodski, SCGP/Stony Brook
John McGreevy, UC San Diego
Prineha Narang, Harvard
Ying Ran, Boston College
Shinsei Ryu, Chicago
Cumrun Vafa, Harvard
Chong Wang, Perimeter
Zhenghan Wang, Microsoft Station Q

9/11/2019 Random Matrix
2019-09-11 13:45 - 14:45 | MA

9/12/2019 Spacetime Seminar
2019-09-12 14:30 - 16:00 | MA

Spacetime and Quantum Mechanics Seminar
2019-09-12 17:38 | MA
As part of the program on Spacetime and Quantum Mechanics, the CMSA will be hosting a weekly seminar on Thursdays at 2:30pm in room G10.

Date
Speaker
Title/Abstract

9/12/2019
Pasha Pylyavskyy (University of Minnesota)
Title: Vector-relation configurations and plabic graphs

19/18/2019
2:00pm
G02
Francis Brown (University of Oxford)
Title: Amplitudes, Polylogs and Moduli Spaces

9/19/2019
Chuck Doran (University of Alberta)
Title: Calabi-Yau geometry of the N-loop sunset Feynman integrals
Abstract: I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals.
Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli.
These include: (1) an iterated fibration structure which allows one to “bootstrap” both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (“jump loci”) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via “creative telescoping”; and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties.
Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev.

9/26/2019
Tomasz Taylor (Northeastern)
Title: Celestial Amplitudes

10/3/2019
Simon Caron-Huot (McGill)
Title: Poincare Duals of Feynman Integrals

10/10/2019
3:30pm
Yutin Huang (National Taiwan University)
Title: Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian

10/15/2019
Tuesday
3:30pm

Sergey Fomin (Univ. of Michigan)

Title: “Morsifications and mutations” (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston).

10/18/2019
Friday
G02
Sebastian Franco (The City College of New York)
Title: Graded quivers, generalized dimer models, and topic geometry

10/31/2019
Junjie Rao (Albert Einstein Institute)
Title: All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity

11/1/2019
SC 232
1:30pm
George Lusztig (MIT)
Title: Total positivity in Springer fibres

11/12/2019
Tuesday
G02
3:30pm

Pierpaolo Mastrolia (University of Padova)
Title: Feynman Integrals and Intersection Theory

11/14/2019
G02
Pierpaolo Mastrolia (University of Padova)
Title: Feynman Integrals and Intersection Theory Pt. II

11/21/2019
Cristian Vergu (Niels Bohr Institute)
Title: The Octagonal Alphabet

11/26/2019
Stephan Stieberger (IAS)
Title: Strings on the Celestial Sphere

12/4/2019
Hadleigh Frost (Oxford)
Title: BCJ numerators, $mathcal{M}_{0,n}$, and ABHY
Abstract: We relate the BCJ numerator Jacobi property to the classical fact that the top homology group of $mathcal{M}_{0,n}$ is isomorphic to a component of the free Lie algebra. We describe ways to get BCJ numerators, and caution that the BCJ Jacobi property doesn’t imply the existence of what has been called a ‘kinematic algebra.’

12/5/2019
David Kosower (IAS)
Title: From scattering amplitudes to classical observables

12/10/2019
Ramis Movassagh (MIT)
Title: Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law
Abstract: In recent years, there has been a surge of activities in proposing “exactly solvable” quantum spin chains with surprising high amount of ground state entanglement–exponentially more than the critical systems that have $log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and ‘generic’ aspects of local spin chains.
