9/28/2021 Combinatorics, Physics and Probability Seminar
2021-09-28 13:00 (America/New_York)
Title: The hypersimplex and the m=2 amplituhedron
Abstract: I’ll discuss a curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way, we prove the sign-flip description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers (inspired by an analogous hypersimplex decomposition).

The Mirror Clemens-Schmid Sequence
2021-09-28 13:00 - 14:00
Abstract: I will present a four-term exact sequence relating the cohomology of a fibration to the cohomology of an open set obtained by removing the preimage of a general linear section of the base. This exact sequence respects three filtrations, the Hodge, weight, and perverse Leray filtrations, so that it is an exact sequence of mixed Hodge structures on the graded pieces of the perverse Leray filtration. I claim that this sequence should be thought of as a mirror to the Clemens-Schmid sequence describing the structure of a degeneration and formulate a “mirror P=W” conjecture relating the filtrations on each side. Finally, I will present evidence for this conjecture coming from the K3 surface setting. This is joint work with Charles F. Doran.

Oscillations in the thermal conductivity of a spin liquid*
2021-09-29 11:48 - 13:48 | Virtual
Title: Oscillations in the thermal conductivity of a spin liquid*
Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.
*Czajka et al., Nature Physics 17, 915 (2021).
Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

Constructions in combinatorics via neural networks
2021-09-29 15:00 - 16:00
Speaker: Adam Wagner, Tel Aviv University
Title: Constructions in combinatorics via neural networks
Abstract: Recently, significant progress has been made in the area of machine learning algorithms, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go, purely through self-play. In this talk I will give a very basic introduction to neural networks and reinforcement learning algorithms. I will also indicate how these methods can be adapted to the ““game” of trying to find a counterexample to a mathematical conjecture, and show some examples where this approach was successful.

Langlands duality for 3 manifolds
2021-09-29 17:15 - 18:15 | Virtual
Speaker: David Jordan (U Edinburgh)
Title: Langlands duality for 3 manifolds
Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten. However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.
In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.
Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

Cytoskeletal Energetics and Energy Metabolism
2021-09-30 13:00 - 14:30
Abstract: Life is a nonequilibrium phenomenon. Metabolism provides a continuous flux of energy that dictates the form and function of many subcellular structures. These subcellular structures are active materials, composed of molecules which use chemical energy to perform mechanical work and locally violate detailed balance. One of the most dramatic examples of such a self-organizing structure is the spindle, the cytoskeletal based assembly which segregates chromosomes during cell division. Despite its central role, very little is known about the nonequilibrium thermodynamics of active subcellular matter, such as the spindle. In this talk, I will describe ongoing work from my lab aimed at understanding the flows of energy which drive the nonequilibrium behaviors of the cytoskeleton in vitro and in vivo.

Instability of naked singularities in general relativity
2021-10-01 09:30 - 10:30
Member Seminar
Speaker: Jue Liu
Title: Instability of naked singularities in general relativity
Abstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture, proposed by Penrose, which roughly states that for generic physical spacetime, the singularities (if existed) must be hidden behind the black holes. Unfortunately, the singularities visible to faraway observers, which are called by naked singularities, indeed exist. The first example constructed by Christodoulou in 1994 is a family of self-similar spherically symmetric spacetime, in which the naked singularity forms due to a self-gravitating scalar field. Therefore the suitable censorship conjecture should be reduced to prove the instability of the naked singularities. In 1999 Christodoulou succeeded to prove the weak cosmic censorship conjecture in spherically symmetric cases, and recently the co-author and I found that the corresponding results have a big probability to be extended to spacetime without symmetries. In this talk I will discuss how to prove the instability of naked singularities using the energy method, and it is this wild method that helps us to extend some results to the asymmetric cases.

Static vacuum extensions of Bartnik boundary data near flat domains
2021-10-01 09:30 - 10:30
Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes. Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.

Math Science Lectures in Honor of Raoul Bott
2021-10-04 02:51 - 2021-10-05 02:51 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
On October 4th and October 5th, 2021, Harvard CMSA will host its annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker will be Michael Freedman (Microsoft). The lectures will take place from 11:00am – 12:15pm (ET) on Zoom.
This will be the third annual lecture series held in honor of Raoul Bott.

Lecture 1
October 4th, 11:00am (Boston time)
Title: The Universe from a single Particle
Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Video

Lecture 2
October 5th, 11:00am (Boston time)
Title: Controlled Mather Thurston Theorems.
Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
Video

Math Science Lectures in Honor of Raoul Bott: Michael Freedman
2021-10-04 11:00 - 12:30 | Virtual
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.
This will be the third annual lecture series held in honor of Raoul Bott.

Lecture 1
October 4th, 11:00am (Boston time)
Title: The Universe from a single Particle
Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Video

Lecture 2
October 5th, 11:00am (Boston time)
Title: Controlled Mather Thurston Theorems.
Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
Video

Angular momentum in general relativity
2021-10-05 08:30 - 09:30
Abstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960′, due to the discovery of “supertranslation ambiguity”: the angular momentums recorded by two distant observers of the same system may not be the same. In this talk, I shall show how the mathematical theory of optimal isometric embedding and quasilocal angular momentum identifies a correction term, and leads to a new definition of angular momentum that is free of any supertranslation ambiguity. This is based on joint work with Po-Ning Chen, Jordan Keller, Ye-Kai Wang, and Shing-Tung Yau.

10/5/2021 Combinatorics, Physics and Probability Seminar
2021-10-05 09:00 - 10:00
Title: Geodesic Geometry on Graphs
Abstract: In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w.
We’ll discuss the concept of graph metrizability, and, in particular, we’ll see that while metrizability is a rare property, there exists infinitely many 2-connected metrizable graphs.
Joint work with Nati Linial.

Strings, knots and quivers
2021-10-06 09:30 - 10:30 | Virtual
Speaker: Piotr Sułkowski (University of Warsaw)
Title: Strings, knots and quivers
Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

Line defects in CFTs: Renormalization group flows and semiclassical limits
2021-10-06 11:49 - 13:49 | Virtual
Title: Line defects in CFTs: Renormalization group flows and semiclassical limits
Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion. For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.

New results in Supergravity via ML Technology
2021-10-06 15:00 - 16:00
Speaker: Thomas Fischbacher, Google
Title: New results in Supergravity via ML Technology
Abstract: The infrastructure built to power the Machine Learning revolution has many other uses beyond Deep Learning. Starting from a general architecture-level overview over the lower levels of Google’s TensorFlow machine learning library, we review how this has recently helped us to find all the stable vacua of SO(8) Supergravity in 3+1 dimensions, has allowed major progress on other related questions about M theory, and briefly discuss other applications in field theory and beyond.

A tour of categorical symmetry
2021-10-07 11:54 - 13:54 | Virtual
Title: A tour of categorical symmetry
Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.

A mirror theorem for GLSMs
2021-10-07 13:00 - 14:00
Abstract: A gauged linear sigma model (GLSM) consists roughly of a complex vector space V, a group G acting on V, a character theta of G, and a G-invariant function w on V. This data defines a GIT quotient Y = [V //_theta G] and a function on that quotient. GLSMs arise naturally in a number of contexts, for instance as the mirrors to Fano manifolds and as examples of noncommutative crepant resolutions. GLSMs provide a broad setting in which it is possible to define an enumerative curve counting theory, simultaneously generalizing FJRW theory and the Gromov-Witten theory of hypersurfaces. Despite a significant effort to rigorously define the enumerative invariants of a GLSM, very few computations of these invariants have been carried out. In this talk I will describe a new method for computing generating functions of GLSM invariants. I will explain how these generating functions arise as derivatives of generating functions of Gromov-Witten invariants of Y.

10/7/2021 Interdisciplinary Science Seminar
2021-10-07 18:41
Title: SiRNA Targeting TCRb: A Proposed Therapy for the Treatment of Autoimmunity
Abstract: As of 2018, the United States National Institutes of Health estimate that over half a billion people worldwide are affected by autoimmune disorders. Though these conditions are prevalent, treatment options remain relatively poor, relying primarily on various forms of immunosuppression which carry potentially severe side effects and often lose effectiveness over time. Given this, new forms of therapy are needed. To this end, we have developed methods for the creation of small-interfering RNA (siRNA) for hypervariable regions of the T-cell receptor β-chain gene (TCRb) as a highly targeted, novel means of therapy for the treatment of autoimmune disorders.
This talk will review the general mechanism by which autoimmune diseases occur and discuss the pros and cons of conventional pharmaceutical therapies as they pertain to autoimmune disease treatment. I will then examine the rational and design methodology for the proposed siRNA therapy and how it contrasts with contemporary methods for the treatment of these conditions. Additionally, the talk will compare the efficacy of multiple design strategies for such molecules by comparison over several metrics and discuss how this will be guiding future research.

UV/IR and Effective Field Theory
2021-10-07 20:30 - 22:00
Speaker: Nima Arkani-Hamed (IAS Princeton)
Title: UV/IR and Effective Field Theory

Causality Comparison and Postive Mass
2021-10-08 09:30 - 10:30
Speaker: Xiaoning Wu, Chinese Academy of Sciences
Title: Causality Comparison and Postive Mass
Abstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity

Knowledge Graph Embeddings and Inference
2021-10-08 09:30 - 10:30
Member Seminar
Speaker: Michael Douglas
Title: Knowledge Graph Embeddings and Inference
Abstract: A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph. Two examples are Wikidata for general knowledge and SemMedDB for biomedical data.
A popular KG representation method is graph embedding, which facilitates question answering, inferring missing edges, and logical reasoning tasks. In this talk we introduce the topic and explain relevant mathematical results on graph embedding. We then analyze KG inference into several mechanisms: motif learning, network learning, and unstructured statistical inference, and describe experiments to measure the contributions of each mechanism.
Joint work with M. Simkin, O. Ben-Eliezer, T. Wu, S. P. Chin, T. V. Dang and A. Wood.

10/12/2021 Combinatorics, Physics and Probability Seminar
2021-10-12 09:00 - 10:00
Title: On counting algebraically defined graphs
Abstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane), the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials), and this lower bound essentially matches the upper bound from Warren’s theorem.

Derived projectivizations of two-term complexes
2021-10-12 13:00 - 14:00
Abstract: For a given two-term complex of vector bundles on a derived scheme (or stack), there are three natural ways to define its “derived projectivizations”: (i) as the derived base-change of the classical projectivization of Grothendieck; (ii) as the derived moduli parametrizing one-dimensional locally free quotients; (iii) as the GIT quotient of the total space by $mathbb{G}_m$-action. In this talk, we first show that these three definitions are equivalent. Second, we prove a structural theorem about the derived categories of derived projectivizations and study the corresponding mutation theory. Third, we apply these results to various moduli situations, including the moduli of certain stable pairs on curves and the Hecke correspondences of one-point modification of moduli of stable sheaves on surfaces. If time allowed, we could also discuss the generalizations of these results to the derived Quot schemes of locally free quotients.

Some remarks on contact Calabi-Yau 7-manifolds
2021-10-13 03:00 - 04:00
Abstract: In geometry and physics it has proved useful to relate G2 and Calabi-Yau geometry via circle bundles. Contact Calabi-Yau 7-manifolds are, in the simplest cases, such circle bundles over Calabi-Yau 3-orbifolds. These 7-manifolds provide testing grounds for the study of geometric flows which seek to find torsion-free G2-structures (and thus Ricci flat metrics with exceptional holonomy). They also give useful backgrounds to examine the heterotic G2 system (also known as the G2-Hull-Strominger system), which is a coupled set of PDEs arising from physics that involves the G2-structure and gauge theory on the 7-manifold. I will report on recent progress on both of these directions in the study of contact Calabi-Yau 7-manifolds, which is joint work with H. Sá Earp and J. Saavedra.

Knot homology and sheaves on the Hilbert scheme of points on the plane
2021-10-13 09:30 - 10:30
Speaker: Alexei Oblomkov (University of Massachusetts)
Title: Knot homology and sheaves on the Hilbert scheme of points on the plane
Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane. The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

Computer-Aided Mathematics and Satisfiability
2021-10-13 14:00 - 15:00
Speaker: Marijn Heule, Carnegie Mellon University
Title: Computer-Aided Mathematics and Satisfiability
Abstract: Progress in satisfiability (SAT) solving has made it possible to determine the correctness of complex systems and answer long-standing open questions in mathematics. The SAT solving approach is completely automatic and can produce clever though potentially gigantic proofs. We can have confidence in the correctness of the answers because highly trustworthy systems can validate the underlying proofs regardless of their size. We demonstrate the effectiveness of the SAT approach by presenting some recent successes, including the solution of the Boolean Pythagorean Triples problem, computing the fifth Schur number, and resolving the remaining case of Keller’s conjecture. Moreover, we constructed and validated a proof for each of these results. The second part of the talk focuses on notorious math challenges for which automated reasoning may well be suitable. In particular, we discuss our progress on applying SAT solving techniques to the chromatic number of the plane (Hadwiger-Nelson problem), optimal schemes for matrix multiplication, and the Collatz conjecture.

D3C: Reducing the Price of Anarchy in Multi-Agent Learning
2021-10-14 09:00 - 10:00 | Virtual
Speaker: Ian Gemp, DeepMind
Title: D3C: Reducing the Price of Anarchy in Multi-Agent Learning
Abstract: In multi-agent systems the complex interaction of fixed incentives can lead agents to outcomes that are poor (inefficient) not only for the group but also for each individual agent. Price of anarchy is a technical game theoretic definition introduced to quantify the inefficiency arising in these scenarios– it compares the welfare that can be achieved through perfect coordination against that achieved by self-interested agents at a Nash equilibrium. We derive a differentiable upper bound on a price of anarchy that agents can cheaply estimate during learning. Equipped with this estimator agents can adjust their incentives in a way that improves the efficiency incurred at a Nash equilibrium. Agents adjust their incentives by learning to mix their reward (equiv. negative loss) with that of other agents by following the gradient of our derived upper bound. We refer to this approach as D3C. In the case where agent incentives are differentiable D3C resembles the celebrated Win-Stay Lose-Shift strategy from behavioral game theory thereby establishing a connection between the global goal of maximum welfare and an established agent-centric learning rule. In the non-differentiable setting as is common in multiagent reinforcement learning we show the upper bound can be reduced via evolutionary strategies until a compromise is reached in a distributed fashion. We demonstrate that D3C improves outcomes for each agent and the group as a whole on several social dilemmas including a traffic network exhibiting Braess’s paradox a prisoner’s dilemma and several reinforcement learning domains.

Stochastic PDE as scaling limits of interacting particle systems
2021-10-14 13:00 - 14:30
Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models. In this talk, I will illustrate how this challenge can be overcome by elucidating the probabilistic connections between models of different levels of detail. These connections explain how stochastic partial differential equations (SPDE) arise naturally from particle models.
I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics.

Peeling properties of the spinor fields and the solutions to nonlinear Dirac equations
2021-10-15 09:30 - 10:30
Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles. We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.

C-P-T Fractionalization, and Quantum Criticality Beyond the Standard Model
2021-10-15 09:30 - 10:30
Member Seminar
Speaker: Juven Wang
Title: C-P-T Fractionalization, and Quantum Criticality Beyond the Standard Model
Abstract: Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F, these symmetries can be further fractionalized forming nonabelian C-P-R-T-(−1)^F group structures, in various examples such as relativistic Lorentz invariant Dirac spinor quantum field theories (QFT), or nonrelativistic quantum many-body systems (involving Majorana zero modes). This result answers Prof. Shing-Tung Yau’s question on “Can C-P-T symmetries be fractionalized more than involutions?” based on arxiv:2109.15320.
In the second part of my talk, I will sketch to explain how can we modify the so(10) Grand Unified Theory (GUT) by adding a new topological term such that two GUTs of Georgi-Glashow and Pati-Salam can smoother into each other in a quantum phase transition, where the Standard Model and new dark sector physics can occur naturally near the critical region. The new modified so(10) GUT requires a double Spin structure that we name DSpin. This phenomenon is inspired by the “deconfined quantum criticality” in condensed matter. Based on arxiv:2106.16248.
