CMSA

General Relativity Conference
2022-04-04 09:30 - 2022-04-08 17:00 (America/New_York) | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Schedule | April 4–8, 2022
Monday, April 4, 2022

Time (ET)
Speaker
Title/Abstract

9:30 am–10:30 am
Pieter Blue, University of Edinburgh, UK
(virtual)
Title: Linear stability of the Kerr spacetime in the outgoing radiation gauge
Abstract: This talk will discuss a new gauge condition (i.e. coordinate condition) for the Einstein equation, the linearisation of the Einstein equation in this gauge, and the decay of solutions to the linearised Einstein equation around Kerr black holes in this gauge. The stability of the family of Kerr black holes under the evolution generated by the Einstein equation is a long-standing problem in mathematical relativity. In 1972, Teukolsky discovered equations governing certain components of the linearised curvature that are invariant under linearised gague transformations. In 1975, Chrzanowski introduced the “outgoing radiation gauge”, a condition on the linearised metric that allows for the construction of the linearised metric from the linearised curvature. In 2019, we proved decay for the metric constructed using Chrzanowski’s outgoing radiation gauge. Recently, using a flow along null geodesics, we have constructed a new gauge such that, in this gauge, the Einstein equation is well posed and such that the linearisation is Chrzanowski’s outgoing radiation gauge.
This is joint work with Lars Andersson, Thomas Backdahl, and Siyuan Ma.

10:30 am–11:30 am
Peter Hintz, ETH Zürich
(virtual)
Title: Mode stability and shallow quasinormal modes of Kerr-de Sitter
black holesAbstract: The Kerr-de Sitter metric describes a rotating black hole with mass $m$ and specific angular momentum $a$ in a universe, such as our own, with cosmological constant $Lambda>0$. I will explain a proof of mode stability for the scalar wave equation on Kerr-de Sitter spacetimes in the following setting: fixing $Lambda$ and the ratio $|a/m|<1$ (related to the subextremality of the black hole in question), mode stability holds for sufficiently small black hole mass $m$. We also obtain estimates for the location of quasinormal modes (resonances) $sigma$ in any fixed half space $Imsigma>-C$. Our results imply that solutions of the wave equation decay exponentially in time to constants, with an explicit exponential rate. The proof is based on careful uniform estimates for the spectral family in the singular limit $mto 0$ in which, depending on the scaling, the Kerr-de Sitter spacetime limits to a Kerr or the de Sitter spacetime.

11:30 am–12:30 pm
Lars Andersson, Albert Einstein Institute, Germany
(virtual)
Title: Gravitational instantons and special geometry
Abstract: Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. In this talk, I will introduce some notions of special geometry, discuss known examples, and mention some open questions. The Chen-Teo gravitational instanton is an asymptotically flat, toric, Ricci flat family of metrics on $mathrm{CP}^2 setminus mathrm{S}^1$, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. I will sketch a proof that the Chen-Teo Instanton is Hermitian and non-Kähler. Thus, all known examples of gravitational instantons are Hermitian. This talks is based on joint work with Steffen Aksteiner, cf. https://arxiv.org/abs/2112.11863.

12:30 pm–1:30 pm
break

1:30 pm–2:30 pm
Martin Taylor, Imperial College London
(virtual)
Title: The nonlinear stability of the Schwarzschild family of black holes
Abstract: I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes. The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family. This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.

2:30 pm–3:30 pm
Po-Ning Chen, University of California, Riverside
(virtual)
Title: Angular momentum in general relativity

Abstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960s, due to the ‘supertranslation ambiguity’. In this talk, we will discuss how the mathematical theory of quasilocal mass and angular momentum leads to a new definition of angular momentum at null infinity that is free of any supertranslation ambiguity.This is based on joint work with Jordan Keller, Mu-Tao Wang, Ye-Kai Wang, and Shing-Tung Yau.

3:30 pm–4:00 pm
break

4:00 pm–5:00 pm
Dan Lee, Queens College (CUNY)
(hybrid: in person & virtual)
Title: Stability of the positive mass theorem
Abstract: We will discuss the problem of stability for the rigidity part of the Riemannian positive mass theorem, focusing on recent work with Kazaras and Khuri, in which we proved that if one assumes a lower Ricci curvature bound, then stability holds with respect to pointed Gromov-Hausdorff convergence.

Tuesday, April 5, 2022

Time (ET)
Speaker
Title/Abstract

9:30 am–10:30 am
Xinliang An, National University of Singapore
(virtual)
Title: Anisotropic dynamical horizons arising in gravitational collapse
Abstract: Black holes are predicted by Einstein’s theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being and about the structures of their inner spacetime singularities. In this talk, we will present several results in these directions. First, in a joint work with Qing Han, with tools from scale-critical hyperbolic method and non-perturbative elliptic techniques, with anisotropic characteristic initial data we prove that: in the process of gravitational collapse, a smooth and spacelike apparent horizon (dynamical horizon) emerges from general (both isotropic and anisotropic) initial data. This result extends the 2008 Christodoulou’s monumental work and it connects to black hole thermodynamics along the apparent horizon. Second, in joint works with Dejan Gajic and Ruixiang Zhang, for the spherically symmetric Einstein-scalar field system, we derive precise blow-up rates for various geometric quantities along the inner spacelike singularities. These rates obey polynomial blow-up upper bounds; and when it is close to timelike infinity, these rates are not limited to discrete finite choices and they are related to the Price’s law along the event horizon. This indicates a new blow-up phenomenon, driven by a PDE mechanism, rather than an ODE mechanism. If time permits, some results on fluid dynamics will also be addressed.

10:30 am–11:30 am
Sergiu Klainerman, Princeton
(virtual)
Title: Nonlinear stability of slowly rotating Kerr solutions
Abstract: I will talk about the status of the stability of Kerr conjecture in General Relativity based on recent results obtained in collaboration with Jeremie Szeftel and Elena Giorgi.

11:30 am–12:30 pm
Siyuan Ma, Sorbonne University
(virtual)
Title: Sharp decay for Teukolsky master equation
Abstract: I will talk about joint work with L. Zhang on deriving the late time dynamics of the spin $s$ components that satisfy the Teukolsky master equation in Kerr spacetimes.

12:30 pm–1:30 pm
Break

1:30 pm–2:30 pm
Jonathan Luk, Stanford
(virtual)
Title: A tale of two tails
Abstract: Motivated by the strong cosmic censorship conjecture, we introduce a general method for understanding the late-time tail for solutions to wave equations on asymptotically flat spacetimes in odd spatial dimensions. A particular consequence of the method is a re-proof of Price’s law-type results, which concern the sharp decay rate of the late-time tails on stationary spacetimes. Moreover, we show that the late-time tails are in general different from the stationary case in the presence of dynamical and/or nonlinear perturbations. This is a joint work with Sung-Jin Oh (Berkeley).

2:30 pm–3:30 pm
Gary Horowitz, University of California Santa Barbara
(virtual)
Title: A new type of extremal black hole
Abstract: I describe a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with a nondegenerate event horizon. Since the surface gravity is nonzero, if quantum matter is added, Hawking radiation does not appear to stop when this new extremal limit is reached. This raises the question of whether Hawking radiation will cause the black hole to turn into a naked singularity. I will argue that does not occur.

3:30 pm–4:00 pm
Break

4:00 pm–5:00 pm
Lydia Bieri, University of Michigan
(virtual)
Title: Gravitational radiation in general spacetimes
Abstract: Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.

Wednesday, April 6, 2022

Time (ET)
Speaker
Title/Abstract

9:30 am–10:30 am
Gerhard Huisken, Mathematisches Forschungsinstitut Oberwolfach
(virtual)
Title: Space-time versions of inverse mean curvature flow
Abstract: In order to extend the Penrose inequality from a time-symmetric setting to general asymptotically flat initial data sets several anisotropic generalisations of inverse mean curvature flow have been suggested that take the full space-time geometry into account. The lecture describes the properties of such flows and reports on recent joint work with Markus Wolff on inverse flow along the space-time mean curvature.

10:30 am–11:30 am
Carla Cederbaum, Universität Tübingen, Germany
(virtual)
Title: Coordinates are messy
Abstract: Asymptotically Euclidean initial data sets $(M,g,K)$ are characterized by the existence of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ decay to the Euclidean metric $delta$ and to $0$ suitably fast, respectively. Provided their matter densities satisfy suitable integrability conditions, they have well-defined (ADM-)energy, (ADM-)linear momentum, and (ADM-)mass. This was proven by Bartnik using harmonic coordinates. To study their (ADM-)angular momentum and (BORT-)center of mass, one usually assumes the existence of Regge—Teitelboim coordinates on the initial data set $(M,g,K)$ in question. We will give examples of asymptotically Euclidean initial data sets which do not possess any Regge—Teitelboim coordinates We will also show that harmonic coordinates can be used as a tool in checking whether a given asymptotically Euclidean initial data set possesses Regge—Teitelboim coordinates. This is joint work with Melanie Graf and Jan Metzger. We will also explain the consequences these findings have for the definition of the center of mass, relying on joint work with Nerz and with Sakovich.

11:30 am–12:30 pm
Stefanos Aretakis, University of Toronto
(virtual)
Title: Observational signatures for extremal black holes
Abstract: We will present results regarding the asymptotics of scalar perturbations on black hole backgrounds. We will then derive observational signatures for extremal black holes that are based on global or localized measurements on null infinity. This is based on joint work with Gajic-Angelopoulos and ongoing work with Khanna-Sabharwal.

12:30 pm–1:30 pm
Break

1:30 pm–2:30 pm
Jared Speck, Vanderbilt University
(virtual)
Title: The mathematical theory of shock waves in multi-dimensional relativistic and non-relativistic compressible Euler flow
Abstract: In the last two decades, there have been dramatic advances in the rigorous mathematical theory of shock waves in solutions to the relativistic Euler equations and their non-relativistic analog, the compressible Euler equations. A lot of the progress has relied on techniques that were developed to study Einstein’s equations. In this talk, I will provide an overview of the field and highlight some recent progress on problems without symmetry or irrotationality assumptions. I will focus on results that reveal various aspects of the structure of the maximal development of the data and the corresponding implications for the shock development problem, which is the problem of continuing the solution weakly after a shock. I will also describe various open problems, some of which are tied to the Einstein–Euler equations. Various aspects of this program are joint with L. Abbrescia, M. Disconzi, and J. Luk.

2:30 pm–3:30 pm
Lan-Hsuan Huang, University of Connecticut
(virtual)
Title: Null perfect fluids, improvability of dominant energy scalar, and Bartnik mass minimizers
Abstract: We introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability. In particular, we prove that a non-improvable initial data set without local symmetries must sit inside a null perfect fluid spacetime carrying a global Killing vector field. We also show that the dominant energy scalar is always almost improvable in a precise sense. Using these main results, we provide a characterization of Bartnik mass minimizing initial data sets which makes substantial progress toward Bartnik’s stationary conjecture.
Along the way we observe that in dimensions greater than eight there exist pp-wave counterexamples (without the optimal decay rate for asymptotically flatness) to the equality case of the spacetime positive mass theorem. As a consequence, we find counterexamples to Bartnik’s stationary and strict positivity conjectures in those dimensions. This talk is based on joint work with Dan A. Lee.

3:30 pm–4:00 pm
Break

4:00 pm–5:00 pm
Demetre Kazaras, Duke University
(virtual)
Title: Comparison geometry for scalar curvature and spacetime harmonic functions
Abstract: Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson toric band inequality, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant inversely proportional to the scalar curvature’s minimum. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions, which recently played the lead role in our recent proof of the positive mass theorem. This is joint work with Sven Hirsch, Marcus Khuri, and Yiyue Zhang.

Thursday, April 7, 2022

Time (ET)
Speaker
Title/Abstract

9:30 am–10:30 am
Piotr Chrusciel, Universitat Wien
(virtual)
Title: Maskit gluing and hyperbolic mass
Abstract: “Maskit gluing” is a gluing construction for asymptotically locally hyperbolic (ALH) manifolds with negative cosmological constant. I will present a formula for the mass of Maskit-glued ALH manifolds and describe how it can be used to construct general relativistic initial data with negative mass.

10:30 am–11:30 am
Greg Galloway, University of Miami (virtual)
Title: Initial data rigidity and applications
Abstract: We present a result from our work with Michael Eichmair and Abraão Mendes concerning initial data rigidity results (CMP, 2021), and look at some consequences. In a note with Piotr Chruściel (CQG 2021), we showed how to use this result, together with arguments from Chruściel and Delay’s proof of the their hyperbolic PMT result, to obtain a hyperbolic PMT result with boundary. This will also be discussed.

11:30 am–12:30 pm
Pengzi Miao, University of Miami
(virtual)
Title: Some remarks on mass and quasi-local mass
Abstract: In the first part of this talk, I will describe how to detect the mass of asymptotically flat and asymptotically hyperbolic manifolds via large Riemannian polyhedra. In the second part, I will discuss an estimate of the Bartnik quasi-local mass and its geometric implications. This talk is based on several joint works with A. Piubello, and with H.C. Jang.

12:30 pm–1:30 pm
Break

1:30 pm–2:30 pm
Yakov Shlapentokh Rothman, Princeton
(hybrid: in person & virtual)
Title: Self-Similarity and Naked Singularities for the Einstein Vacuum Equations
Abstract: We will start with an introduction to the problem of constructing naked singularities for the Einstein vacuum equations, and then explain our discovery of a fundamentally new type of self-similarity and show how this allows us to construct solutions corresponding to a naked singularity. This is joint work with Igor Rodnianski.

2:30 pm–3:30 pm
Marcelo Disconzi, Vanderbilt University
(virtual)
Title: General-relativistic viscous fluids.
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.

3:30 pm–4:00 pm
Break

4:00 pm–5:00 pm
Maxime van de Moortel, Princeton
(hybrid: in person & virtual)
Title: Black holes: the inside story of gravitational collapse
Abstract: What is inside a dynamical black hole? While the local region near time-like infinity is understood for various models, the global structure of the black hole interior has largely remained unexplored.
These questions are deeply connected to the nature of singularities in General Relativity and celebrated problems such as Penrose’s Strong Cosmic Censorship Conjecture.
I will present my recent resolution of these problems in spherical gravitational collapse, based on the discovery of a novel phenomenon: the breakdown of weak singularities and the dynamical formation of a strong singularity.

Friday, April 8, 2022

Time (ET)
Speaker
Title/Abstract

9:30 am–10:30 am
Ye-Kai Wang, National Cheng Kun University, Taiwan
(virtual)
Title: Supertranslation invariance of angular momentum at null infinity in double null gauge
Abstract: This talk accompanies Po-Ning Chen’s talk on Monday with the results described in the double null gauge rather than Bondi-Sachs coordinates. Besides discussing
how Chen-Wang-Yau angular momentum resolves the supertranslation ambiguity, we also review the definition of angular momentum defined by A. Rizzi. The talk is based on the joint work with Po-Ning Chen, Jordan Keller, Mu-Tao Wang, and Shing-Tung Yau.

10:30 am–11:30 am
Zoe Wyatt, King’s College London
(virtual)
Title: Global Stability of Spacetimes with Supersymmetric Compactifications
Abstract: Spacetimes with compact directions which have special holonomy, such as Calabi-Yau spaces, play an important role in
supergravity and string theory. In this talk I will discuss a recent work with Lars Andersson, Pieter Blue and Shing-Tung Yau, where we show the global, nonlinear stability a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This stability result is related to a conjecture of Penrose concerning the validity of string theory. Our proof uses the intersection of methods for quasilinear wave and Klein-Gordon equations, and so towards the end of the talk I will also comment more generally on coupled wave–Klein-Gordon equations.

11:30 am–12:30 pm
Elena Giorgi, Columbia University
(hybrid: in person & virtual)
Title: The stability of charged black holes
Abstract: Black hole solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

12:30 pm–1:30 pm
Break

1:30 pm–2:30 pm
Marcus Khuri, Stony Brook University
(virtual)
Title: The mass-angular momentum inequality for multiple black holes

Abstract: Consider a complete 3-dimensional initial data set for the Einstein equations which has multiple asymptotically flat or asymptotically cylindrical ends. If it is simply connected, axisymmetric, maximal, and satisfies the appropriate energy condition then the ADM mass of any of the asymptotically flat ends is bounded below by the square root of the total angular momentum. This generalizes previous work of Dain, Chrusciel-Li-Weinstein, and Schoen-Zhou which treated either the single black hole case or the multiple black hole case without an explicit lower bound. The proof relies on an analysis of the asymptotics of singular harmonic maps from
R^3 Gamma –>H^2 where Gamma is a coordinate axis. This is joint work with Q. Han, G. Weinstein, and J. Xiong.

2:30 pm–3:30 pm
Martin Lesourd, Harvard
(hybrid: in person & virtual)
Title: A Snippet on Mass and the Topology and Geometry of Positive Scalar Curvature
Abstract: I will talk about a small corner of the study of Positive Scalar Curvature (PSC) and questions which are most closely related to the Positive Mass Theorem. The classic questions are ”which topologies allow for PSC?” and ”what is the geometry of manifolds with PSC?”. This is based on joint work with Prof. S-T. Yau, Prof. D. A. Lee, and R. Unger.

3:30 pm–4:00 pm
Break

4:00 pm–5:00 pm
Georgios Moschidis, Princeton
(virtual)
Title: Weak turbulence for the Einstein–scalar field system.
Abstract: In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. In the presence of a negative cosmological constant, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity, lead to the formation of black holes after sufficiently long time.
In this talk, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein-scalar field system. The construction of the unstable initial data will require carefully designing a family of initial configurations of localized matter beams and estimating the exchange of energy taking place between interacting beams over long periods of time, as well as estimating the decoherence rate of those beams.

Causality constraints on corrections to Einstein gravity
2022-04-04 10:00 - 23:00 | Virtual
Swampland Seminar
Speakers: Simon Caron-Huot (McGill University) and Julio Parra (Caltech)

Title: Causality constraints on corrections to Einstein gravity

Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

Second Annual Yip Lecture: Extraterrestrial Life
2022-04-04 19:00 - 20:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Harvard CMSA hosted the second annual Yip Lecture on April 4, 2022.
The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.
This year’s speaker was Avi Loeb (Harvard).

Extraterrestrial Life
Abstract: Are we alone? It would be arrogant to think that we are, given that a quarter of all stars host a habitable Earth-size planet. Upcoming searches will aim to detect markers of life in the atmospheres of planets outside the Solar System. We also have unprecedented technologies to detect signs of intelligent civilizations through industrial pollution of planetary atmospheres, space archaeology of debris from dead civilizations or artifacts such as photovoltaic cells that are used to re-distribute light and heat on the surface of a planet or giant megastructures. Our own civilization is starting to explore interstellar travel. Essential information may also arrive as a “message in a bottle”, implying that we should examine carefully any unusual object that arrives to our vicinity from outside the Solar System, such as `Oumuamua.

Abraham (Avi) Loeb is the Frank B. Baird, Jr., Professor of Science at Harvard University and a bestselling author (in lists of the New York Times, Wall Street Journal, Publishers Weekly, Die Zeit, Der Spiegel, L’Express and more). He received a PhD in Physics from the Hebrew University of Jerusalem in Israel at age 24 (1980–1986), led the first international project supported by the Strategic Defense Initiative (1983–1988), and was subsequently a long-term member of the Institute for Advanced Study at Princeton (1988–1993). Loeb has written 8 books, including most recently, Extraterrestrial (Houghton Mifflin Harcourt, 2021), and nearly a thousand papers (with an h-index of 118) on a wide range of topics, including black holes, the first stars, the search for extraterrestrial life, and the future of the Universe. Loeb is the head of the Galileo Project in search for extraterrestrial intelligence, the Director of the Institute for Theory and Computation (2007–present) within the Harvard-Smithsonian Center for Astrophysics, and also serves as the Head of the Galileo Project (2021–present). He had been the longest serving Chair of Harvard’s Department of Astronomy (2011–2020) and the Founding Director of Harvard’s Black Hole Initiative (2016–2021). He is an elected fellow of the American Academy of Arts & Sciences, the American Physical Society, and the International Academy of Astronautics. Loeb is a former member of the President’s Council of Advisors on Science and Technology (PCAST) at the White House, a former chair of the Board on Physics and Astronomy of the National Academies (2018–2021) and a current member of the Advisory Board for “Einstein: Visualize the Impossible” of the Hebrew University. He also chairs the Advisory Committee for the Breakthrough Starshot Initiative (2016–present) and serves as the Science Theory Director for all Initiatives of the Breakthrough Prize Foundation. In 2012, TIME magazine selected Loeb as one of the 25 most influential people in space and in 2020 Loeb was selected among the 14 most inspiring Israelis of the last decade.
Click here for Loeb’s commentaries on innovation and diversity.
Website: https://www.cfa.harvard.edu/~loeb/
See the Harvard Gazette article featuring Avi Loeb: “Oh, if I could talk to the aliens” published March 8, 2022.
Prof. Loeb’s books:
Extraterrestrial: The First Sign of Intelligent Life Beyond Earth (2021)
Life in the Cosmos: From Biosignatures to Technosignatures (2021)
Avil Loeb is the head of the Galileo Project at Harvard.

The previous Yip Lecture featured Peter Galison (Harvard), who spoke on the EHT’s hunt for an objective image of a black hole.

Regularized integrals on Riemann surfaces and correlations functions in 2d chiral CFTs
2022-04-05 09:30 - 10:30 | Virtual
Abstract: I will report a recent approach of regularizing divergent integrals on configuration spaces of Riemann surfaces, introduced by Si Li and myself in arXiv:2008.07503, with an emphasis on genus one cases where modular forms arise naturally. I will then talk about some applications in studying correlation functions in 2d chiral CFTs, holomorphic anomaly equations, etc. If time permits, I will also mention a more algebraic formulation of this notion of regularized integrals in terms of mixed Hodge structures.
The talk is partially based on joint works with Si Li.

What is Mathematical Consciousness Science?
2022-04-06 09:30 - 10:30 | MA
Speaker: Johannes Kleiner, LMU München
Title: What is Mathematical Consciousness Science?
Abstract: In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now called Mathematical Consciousness Science. In this talk, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.

Late time von Neumann entropy and measurement-induced phase transition
2022-04-06 10:30 - 12:00 | Virtual
Youtube Video

Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.

On the wave turbulence theory for a stochastic KdV type equation
2022-04-06 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Random Matrix & Probability Theory Seminar

Speaker: Minh-Binh TRAN (SMU & MIT)

Location: CMSA, Room G02
Title: On the wave turbulence theory for a stochastic KdV type equation
Abstract: We report recent progress, in collaboration with Gigliola Staffilani (MIT), on the problem of deriving kinetic equations from dispersive equations. To be more precise, starting from the stochastic Zakharov-Kuznetsov equation, a multidimensional KdV type equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We show that the two point correlation function can be asymptotically expressed as the solution of the 3-wave kinetic equation at the kinetic limit under very general assumptions: the initial condition is out of equilibrium, the dimension is $dge 2$, the smallness of the nonlinearity $lambda$ is allowed to be independent of the size of the lattice, the weak noise is chosen not to compete with the weak nonlinearity and not to inject energy into the equation. Unlike the cubic nonlinear Schrodinger equation, for which such a general result is commonly expected without the noise, the kinetic description of the deterministic lattice ZK equation is unlikely to happen. One of the key reasons is that the dispersion relation of the lattice ZK equation leads to a singular manifold, on which not only 3-wave interactions but also all m-wave interactions are allowed to happen. This phenomenon has been first observed by Lukkarinen as a counterexample for which one of the main tools to derive kinetic equations from wave equations (the suppression of crossings) fails to hold true.

Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
2022-04-06 21:30 - 22:30 | Virtual
Abstract: Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced theory. These invariants are conjectured to be integers and have alternative interpretations using sheaf theoretic moduli spaces. Our conjecture is proved for the product of two K3 surfaces, which naturally leads to a closed formula of Fujiki constants of Chern classes of tangent bundles of Hilbert schemes of points on K3 surfaces. On a very general holomorphic symplectic 4-folds of K3^[2] type, our conjecture provides a Yau-Zaslow type formula for the number of isolated genus 2 curves of minimal degree. Based on joint works with Georg Oberdieck and Yukinobu Toda.

Lattice Gauge Theory View of Toric Codes, X-cube, and More
2022-04-07 09:30 - 11:00 | Virtual
Youtube Video

Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.
References:
[1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021)
[1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022)
[2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation.
[3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.

Theories of branching morphogenesis
2022-04-07 13:00 - 14:26 | MA
Abstract: The morphogenesis of branched tissues has been a subject of long-standing debate. Although much is known about the molecular pathways that control cell fate decisions, it remains unclear how macroscopic features of branched organs, including their size, network topology and spatial pattern are encoded. Based on large-scale reconstructions of the mouse mammary gland and kidney, we begin by showing that statistical features of the developing branched epithelium can be explained quantitatively by a local self-organizing principle based on a branching and annihilating random walk (BARW). In this model, renewing tip-localized progenitors drive a serial process of ductal elongation and stochastic tip bifurcation that terminates when active tips encounter maturing ducts. Then, based on reconstructions of the developing mouse salivary gland, we propose a generalisation of BARW model in which tips arrested through steric interaction with proximate ducts reactivate their branching programme as constraints become alleviated through the expansion of the underlying mesenchyme. This inflationary branching-arresting random walk model offers a more general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the tissue into which it expands.

The space of vector bundles on spheres: algebra, geometry, topology
2022-04-07 15:22 - 17:22 | MA
Abstract: Bott periodicity relates vector bundles on a topological space X to vector bundles on X “times a sphere”. I’m not a topologist, so I will try to explain an algebraic or geometric incarnation, in terms of vector bundles on the Riemann sphere. I will attempt to make the talk introductory, and (for the most part) accessible to those in all fields, at the expense of speaking informally and not getting far. This relates to recent work of Hannah Larson, as well as joint work with (separately) Larson and Jim Bryan.

Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning
2022-04-08 08:45 - 10:15 | Virtual
Speaker: Jörn Boehnke
Title: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning
Abstract: In the standard regression discontinuity setting, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold. We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units. In the first stage, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score. In the second stage, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest. We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations, and propose the use machine learning algorithms to achieve high prediction accuracy. Finally, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies. We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.

Type IIB flux compactifications with $h^{1,1}=0$
2022-04-11 10:00 - 11:00 | Virtual
Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.

BCFW recursion relations and non-planar positive geometry
2022-04-12 09:30 - 10:30 | MA
Abstract: There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level S-matrix is represented as a sum of planar on-shell diagrams (aka plabic graphs) and associated with logarithmic forms on the Grassmannian cells of certain dimensionality. In this talk, we explore non-adjacent BCFW shifts which naturally lead to non-planar on-shell diagrams and new interesting subspaces inside the real Grassmannian.
**This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.
All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.
LINK TO FORM

Applications of Higher Determinant Map
2022-04-12 11:58 - 12:58 | Virtual
Abstract: In this talk I will explain the construction of a determinant map for Tate objects and two applications: (i) to construct central extensions of iterated loop groups and (ii) to produce a determinant theory on certain ind-schemes. For that I will introduce some aspects of the theory of Tate objects in a couple of contexts.

Quantisation in monoidal categories and quantum operads
2022-04-13 09:30 - 10:30 | MA
Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure. But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups. The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.
In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts.

Why is the mission impossible? Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
2022-04-13 20:30 - 22:00 | Virtual
Youtube Video
Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.
We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.
We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.
Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.

SIMPLEs: a single-cell RNA sequencing imputation strategy preserving gene modules and cell clusters variation
2022-04-14 09:00 - 10:00 | MA
Abstract: A main challenge in analyzing single-cell RNA sequencing (scRNA-seq) data is to reduce technical variations yet retain cell heterogeneity. Due to low mRNAs content per cell and molecule losses during the experiment (called ‘dropout’), the gene expression matrix has a substantial amount of zero read counts. Existing imputation methods treat either each cell or each gene as independently and identically distributed, which oversimplifies the gene correlation and cell type structure. We propose a statistical model-based approach, called SIMPLEs (SIngle-cell RNA-seq iMPutation and celL clustErings), which iteratively identifies correlated gene modules and cell clusters and imputes dropouts customized for individual gene module and cell type. Simultaneously, it quantifies the uncertainty of imputation and cell clustering via multiple imputations. In simulations, SIMPLEs performed significantly better than prevailing scRNA-seq imputation methods according to various metrics. By applying SIMPLEs to several real datasets, we discovered gene modules that can further classify subtypes of cells. Our imputations successfully recovered the expression trends of marker genes in stem cell differentiation and can discover putative pathways regulating biological processes.

Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4
2022-04-14 09:30 - 10:30 | Virtual
Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.

Cancellation of the vacuum energy and Weyl anomaly in the standard model, and a two-sheeted, CPT-symmetric universe
2022-04-14 09:30 - 11:00 | Virtual
Youtube video

Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields. Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos. Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).
As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role. Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times. Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime. This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole). It also makes a number of testable predictions.
(Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)

Workshop on Machine Learning and Mathematical Conjecture
2022-04-15 09:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
On April 15, 2022, the CMSA will hold a one-day workshop, Machine Learning and Mathematical Conjecture, related to the New Technologies in Mathematics Seminar Series.
Location: Room G10, 20 Garden Street, Cambridge, MA 02138.
Organizers: Michael R. Douglas (CMSA/Stony Brook/IAIFI) and Peter Chin (CMSA/BU).
Machine learning has driven many exciting recent scientific advances. It has enabled progress on long-standing challenges such as protein folding, and it has helped mathematicians and mathematical physicists create new conjectures and theorems in knot theory, algebraic geometry, and representation theory.
At this workshop, we will bring together mathematicians, theoretical physicists, and machine learning researchers to review the state of the art in machine learning, discuss how ML results can be used to inspire, test and refine precise conjectures, and identify mathematical questions which may be suitable for this approach.
Speakers:

James Halverson, Northeastern University Dept. of Physics and IAIFI
Fabian Ruehle, Northeastern University Dept. of Physics and Mathematics and IAIFI
Andrew Sutherland, MIT Department of Mathematics

CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Game Theory Basics and Classical Existence Theorems
2022-04-18 09:30 - 11:00 | Virtual
Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians
April 18, 2022 | 9:30 – 11:00 am ET
Title: Game Theory Basics and Classical Existence Theorems
Abstract: Games in extensive and normal form. Equilibrium existence theorems by Nash, von Neumann, and Zermelo
Talk chairs: Scott Kominers, Sergiy Verstyuk
SLIDES | VIDEO

4/18/2022 Swampland Seminar
2022-04-18 13:00 - 14:00 | Virtual
Open mic Swampland Discussion
Topic: Cobordism

Equivariant Verlinde algebra and quantum K-theory of the moduli space of vortices
2022-04-19 09:30 - 10:30 | Virtual
Abstract: In studying complex Chern-Simons theory on a Seifert manifold, Gukov-Pei proposed an equivariant Verlinde formula, a one-parameter deformation of the celebrated Verlinde formula. It computes, among many things, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the Hitchin moduli space. Gukov-Pei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum K-invariants of a non-compact (Kahler) quotient space studied by Hanany-Tong.
In this talk, I will explain the setup of this conjecture and its proof via wall-crossing of moduli spaces of (parabolic) Bradlow-Higgs triples. It is based on work in progress with Wei Gu and Du Pei.

Some combinatorics of Wilson loop diagrams
2022-04-19 09:30 - 10:30 | Hybrid
Abstract: Wilson loop diagrams can be used to study amplitudes in N=4 SYM. I will set them up and talk about some of their combinatorial aspects, such as how many Wilson loop diagrams give the same positroid and how to combinatorially read off the dimension and the denominators for the integrands.
**This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.
All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.
LINK TO FORM

CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Mechanism Design
2022-04-20 09:30 - 11:00 | Virtual
Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians
April 20, 2022 | 9:30 – 11:00 am ET
Title: Mechanism Design
Abstract: Given a social goal, under what circumstances can we design a game to achieve that goal?
Talk chairs: Scott Kominers, Sergiy Verstyuk
SLIDES | VIDEO

Superconductivity in infinite-layer nickelates
2022-04-20 10:30 - 13:00 | MA
Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.

Secure Multi-Party Computation: from Theory to Practice
2022-04-21 09:00 - 10:00 | MA
Abstract:
Encryption is the backbone of cybersecurity. While encryption can secure data both in transit and at rest, in the new era of ubiquitous computing, modern cryptography also aims to protect data during computation. Secure multi-party computation (MPC) is a powerful technology to tackle this problem, which enables distrustful parties to jointly perform computation over their private data without revealing their data to each other. Although it is theoretically feasible and provably secure, the adoption of MPC in real industry is still very much limited as of today, the biggest obstacle of which boils down to its efficiency.
My research goal is to bridge the gap between the theoretical feasibility and practical efficiency of MPC. Towards this goal, my research spans both theoretical and applied cryptography. In theory, I develop new techniques for achieving general MPC with the optimal complexity, bringing theory closer to practice. In practice, I design tailored MPC to achieve the best concrete efficiency for specific real-world applications. In this talk, I will discuss the challenges in both directions and how to overcome these challenges using cryptographic approaches. I will also show strong connections between theory and practice.
Biography:
Peihan Miao is an assistant professor of computer science at the University of Illinois Chicago (UIC). Before coming to UIC, she received her Ph.D. from the University of California, Berkeley in 2019 and had brief stints at Google, Facebook, Microsoft Research, and Visa Research. Her research interests lie broadly in cryptography, theory, and security, with a focus on secure multi-party computation — especially in incorporating her industry experiences into academic research.

Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system
2022-04-21 10:00 - 11:00 | MA
Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete. For the proof, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.

CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Auction Theory
2022-04-22 09:30 - 23:00 | Virtual
Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians
April 22, 2022 | 9:30 – 11:00 am ET
Title: Auction Theory
Abstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher).
Talk chairs: Scott Kominers, Sergiy Verstyuk
SLIDES | VIDEO Answers to Questions from Talks 2 and 3
