The 20192020 Colloquium will take place every Wednesday from 4:30 to 5:30 virtually, using zoom. Please email the seminar organizers to obtain a link. 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.
Date  Speaker  Title/Abstract 

1/29/2020 
David Yang (Harvard) 
Abstract: Dataintensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in dataintensive economies: ﬁrst, states are key collectors and repositories of data; second, data is a nonrival input in innovation. We document the importance of statecollected data for innovation using comprehensive data on Chinese facial recognition AI ﬁrms and government contracts. Firms produce more commercial software and patents, particularly dataintensive 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, datadriven industrial policy, and data regulation due to privacy concerns. When the degree of nonrivalry 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 dataintensive economies.

2/5/2020 
Scott Aaronson (UT Austin) 
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” Based on joint work with Guy Rothblum (arXiv:1904.08747) 
2/12/2020 
Scott Kominers (Harvard) 
Title: A Compact, Logical Approach to LargeMarket 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 gametheoretic 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 manoptimal stable matchings in infinite economies, as well as strategyproofness of the manoptimal 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 rightangled 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 3manifolds and simultaneously dramatically extended our understanding of many infinite groups.

3/4/2020 4:45 – 5:45pm 
Salil Vadhan (Harvard) 
Title: Derandomizing Algorithms via Spectral Graph Theory Abstract: Randomization is a powerful tool for algorithms; it is often easier to design efficient algorithms if we allow the algorithms to “toss coins” and output a correct answer with high probability. However, a longstanding conjecture in theoretical computer science is that every randomized algorithm can be efficiently “derandomized” — converted into a deterministic algorithm (which always outputs the correct answer) with only a polynomial increase in running time and only a constantfactor increase in space (i.e. memory usage). In this talk, I will describe an approach to proving the space (as opposed to time) version of this conjecture via spectral graph theory. Specifically, I will explain how randomized spacebounded algorithms are described by random walks on directed graphs, and techniques in algorithmic spectral graph theory (e.g. solving Laplacian systems) have yielded deterministic spaceefficient algorithms for approximating the behavior of such random walks on undirected graphs and Eulerian directed graphs (where every vertex has the same indegree as outdegree). If these algorithms can be extended to general directed graphs, then the aforementioned conjecture about derandomizing spaceefficient algorithms will be resolved. 
3/11/2020 Postponed 
Jose Scheinkman (Columbia) 
This colloquium will be rescheduled at a later date. Title: Menu Costs and the Volatility of Inflation
Abstract: We present a statedependent equilibrium pricing model that generates inflation rate fluctuations from idiosyncratic shocks to the cost of price changes of individual firms. A firm’s nominal price increase lowers other firms’ relative prices, thereby inducing further nominal price increases. We first study a meanfield limit where the equilibrium is characterized by a variational inequality and exhibits a constant rate of inflation. We use the limit model to show that in the presence of a large but finite number n of firms the snowball effect of repricing causes fluctuations to the aggregate price level and these fluctuations converge to zero slowly as n grows. The fluctuations caused by this mechanism are larger when the density of firms at the repricing threshold is high, and the density at the threshold is high when the trend inflation level is high. However a calibration to US data shows that this mechanism is quantitatively important even at modest levels of trend inflation and can account for the positive relationship between inflation level and volatility that has been observed empirically. 
3/12/2020 4:00 – 5:00pm

Daniel Forger (University of Michigan) 
This meeting will be taking place virtually on Zoom. Title: Math, Music and the Mind; Mathematical analysis of the performed Trio Sonatas of J. S. Bach Abstract: I will describe a collaborative project with the University of Michigan Organ Department to perfectly digitize many performances of difficult organ works (the Trio Sonatas by J.S. Bach) by students and faculty at many skill levels. We use these digitizations, and direct representations of the score to ask how music should encoded in the mind. Our results challenge the modern mathematical theory of music encoding, e.g., based on orbifolds, and reveal surprising new mathematical patterns in Bach’s music. We also discover ways in which biophysical limits of neuronal computation may limit performance. Daniel Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan. He is also a visiting scholar at Harvard’s NSFSimons Center and an Associate of the American Guild of Organists. 
3/25/2020 
Cancelled  
4/1/2020 
Mauricio Santillana (Harvard) 
This meeting will be taking place virtually on Zoom. Title: Datadriven machine learning approaches to monitor and predict events in healthcare. From populationlevel disease outbreaks to patientlevel monitoring Abstract: I will describe datadriven machine learning methodologies that leverage Internetbased information from search engines, Twitter microblogs, crowdsourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near realtime. I will also present datadriven machine learning methodologies that leverage continuousintime information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs. 
4/8/2020 
This meeting will be taking place virtually on Zoom.  
4/15/2020 
This meeting will be taking place virtually on Zoom.  
4/22/2020 
This meeting will be taking place virtually on Zoom.  
4/29/2020 
This meeting will be taking place virtually on Zoom.  
5/6/2020 

5/13/2020 

5/20/2020 
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 NijenhuisLie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vectorvalued forms on M. One of these can be applied to distinguish nonisomorphic nonintegrable almost complex structures on M. Another one, the Jcohomology, is familiar in the integrable case but we extend its definition and applicability to the case of nonintegrable almost complex structures. The Jcohomology encodes whether a complex manifold satisfies the “deldelbarlemma”, and more generally in the nonintegrable case the Jcohomology 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.
ChristodoulouKlainerman 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)

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 ArkaniHamed (IAS)

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

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)

Title: An Introduction to the NonPerturbative Bootstrap
Abstract: I will discuss nonperturbative 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.
Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard). 
12/4/2019  XiaoGang Wen (MIT) Video 
Title: Emergence of gravitonlike excitations from a lattice model
Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and gravitonlike excitations. The appearance of vectorlike charge and symmetric tensor field may be related to gapless fracton phases. 