Spring 2020 Colloquium, Wednesdays

The 2019-2020 Colloquium will take place every Wednesday from 4:30 to 5:30 at CMSA, 20 Garden Street, Room G10. This year’s colloquium will be organized by Aghil Alaee, Ryan Thorngren and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed. Information on previous colloquia can be found here.

Spring 2020

Date Speaker Title/Abstract

1/29/2020

David Yang (Harvard)

 
Abstract: Data-intensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in data-intensive economies: first, states are key collectors and repositories of data; second, data is a non-rival input in innovation. We document the importance of state-collected data for innovation using comprehensive data on Chinese facial recognition AI firms and government contracts. Firms produce more commercial software and patents, particularly data-intensive ones, after receiving government public security contracts. Moreover, effects are largest when contracts provide more data. We then build a directed technical change model to study the state’s role in three applications: autocracies demanding AI for surveillance purposes, data-driven industrial policy, and data regulation due to privacy concerns. When the degree of non-rivalry is as strong as our empirical evidence suggests, the state’s collection and processing of data can shape the direction of innovation and growth of data-intensive economies.

2/5/2020

Scott Aaronson (UT Austin)

Video

Title: Gentle Measurement of Quantum States and Differential Privacy

Abstract: I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography”
of quantum states (that is, answering a large number of questions about a quantum state given few copies of it).

Based on joint work with Guy Rothblum (arXiv:1904.08747)

2/12/2020

Scott Kominers (Harvard)

Title: A Compact, Logical Approach to Large-Market Analysis

Abstract: In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

2/19/2020

Peter Shor (MIT)

Title: Quantum Money from Lattices 

Abstract: Quantum money is  a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure. 

2/26/2020

Daneil Wise (McGill) Title: The Cubical Route to Understanding Groups
 
 
Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds and simultaneously dramatically extended our understanding of many infinite groups. 

3/4/2020

Salil Vadhan (Harvard) TBA

3/11/2020

Jun Liu (Harvard) TBA

3/18/2020

   

3/25/2020

   

4/1/2019

CancelledYip Lecture

   

4/8/2019

   

4/15/2019

   

4/22/2019

   

4/29/2019

   

5/6/2019

   

5/13/2019

   

5/20/2019

   

Fall 2019

Date Speaker Title/Abstract
9/18/2019 Bill Helton (UC San Diego) Title:  A taste of noncommutative convex algebraic geometry 

 

 

Abstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example,

◦ A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials.

◦ A convex NC semialgebraic set has a linear matrix inequality representation. 

◦ The natural Nullstellensatz are falling into place. 

 The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019.  

9/25/2019 Pavel Etingof (MIT)

 

 

 

Title: Double affine Hecke algebras

 

 

Abstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications.

10/2/2019 Spiro Karigiannis (University of Waterloo) Title: Cohomologies on almost complex manifolds and their applications

 

 

Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.

10/9/2019 Hans Lindblad (Johns Hopkins University) Title:  Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition

 

 

 

Abstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition  satisfy the preserved wave coordinate condition.

 

Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times.

John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas  lainerman came up with the ‘null condition’, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition.

Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition.

Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to afraction and has now been used to prove global existence also with matter fields.

Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equationsbackwards to obtain global solutions with given data at infinity.   

10/16/2019 Aram Harrow (MIT)

 

 

Video

Title: Monogamy of entanglement and convex geometry

 

 

Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems.

10/23/2019 No talk  
10/30/2019 Nima Arkani-Hamed (IAS)

 

 

Video

Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity
11/6/2019 Kevin Costello (Perimeter Institute)

 

 

Video

Title: A unified perspective on integrability

 

 

 

Abstract: Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics.   I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu.

11/13/2019 Heather  Harrington (University of Oxford) Title:  Algebra, Geometry and Topology of ERK Enzyme Kinetics

 

 

Abstract: In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

11/20/2019 Xi Yin (Harvard)

 

 

Video

Title: An Introduction to the Non-Perturbative Bootstrap

 

 

Abstract: I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap

11/25/2019

 

 

Monday

Madhu Sudan (Harvard)
 
Abstract: The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits.


In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction.

Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard).

12/4/2019 Xiao-Gang Wen (MIT)
Video
Title: Emergence of graviton-like excitations from a lattice model

 

 

Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases.

 

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