Calendar
- 12September 12, 2021No events
- 13September 13, 2021No events
- 14September 14, 2021
CMSA Algebraic Geometry in String Theory Seminar: Simplices in the Calabi--Yau web
Calabi–Yau manifolds of a given dimension are connected by an intricate web of birational maps. This web has deep consequences for the derived categories of coherent sheaves on such manifolds, and for the associated string theories. In particular, for 4-folds and beyond, I will highlight certain simplices appearing in the web, and identify corresponding derived category structures.
https://harvard.zoom.us/j/98781914555?pwd=bmVzZGdlRThyUDREMExab20ybmg1Zz09
Measuring the irrationality of complete intersections
1 Oxford Street, Cambridge, MA 02138 USAThe classical question of determining which varieties are rational has led to a huge amount of interest and activity. On the other hand, one can take on a complementary perspective: Given a smooth projective variety whose nonrationality is known, how far is it from being rational? I will explain recent progress in this direction for complete intersections in projective space. - 15September 15, 2021
CMSA Colloquium: Hyperbolic Geometry and Quantum Invariants
There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.
Zoom link: https://harvard.zoom.us/j/95767170359?pwd=S0RheFJyMklwall1YnRKN2twcGxxdz09
CMSA Joint Strongly Correlated/High-Tc SC: Three-particle mechanism for pairing and superconductivity
I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.[1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
[2] V. Crepel and L. Fu, arXiv:2103.12060
[3] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020)—–
Subscribe to Harvard CMSA seminar videos (more to be uploaded):
https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274WwFinitely Presented Groups in Arithmetic Geometry
1 Oxford Street, Cambridge, MA 02138 USAWe discuss the problem of determining the number of generators and relations of several profinite groups of arithmetic and geometric origin. These include etale fundamental groups of smooth projective varieties, absolute Galois groups of local fields, and Galois groups of maximal unramified extensions of number fields. The results are based on a cohomological presentability criterion of Lubotzky, and draw inspiration from well-known facts about three-dimensional manifolds, as in arithmetic topology.
The talk is based on a joint work with Esnault and Srinivas, on a joint work with Jarden, and on work of Yuan Liu.
CMSA New Technologies in Mathematics Seminar: Why abstraction is the key to intelligence, and what we're still missing
This talk provides a personal perspective on the way forward towards more human-like and more intelligent artificial systems. Traditionally, symbolic and probabilistic methods have dominated the domains of concept formation, abstraction, and automated reasoning. More recently, deep learning-based approaches have led to significant breakthroughs, including successes in games and combinatorial search tasks. However, the resulting systems are still limited in scope and capabilities — they remain brittle, data-hungry, and their generalization capabilities are limited. We will address a set of questions: why is conceptual abstraction essential for intelligence? What is the nature of abstraction, and its relationship to generalization? What kind of abstraction can deep learning models generate, and where do they fail? What are the methods that are currently successful in generating strong conceptual abstraction? Finally, we will consider how to leverage a hybrid approach to reinforce the strength of different approaches while compensating for their respective weaknesses.
*Special time – normally will be at 2 pm*
https://harvard.zoom.us/j/99651364593?pwd=Q1R0RTMrZ2NZQjg1U1ZOaUYzSE02QT09
- 16September 16, 2021
CMSA Quantum Matter in Mathematics & Physics Seminar: The Hilbert Space of large N Chern-Simons matter theories
We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular, implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit; the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.—–
Subscribe to Harvard CMSA seminar videos (more to be uploaded):
https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274WwCMSA Active Matter Seminar: The many phases of a cell
I will begin by introducing an emerging paradigm of cellular organization – the dynamic compartmentalization of biochemical pathways and molecules by phase separation into distinct and multi-phase condensates. Motivated by this, I will discuss two largely orthogonal problems, united by the theme of phase separation in multi-component and chemically active fluid mixtures.1. I will propose a theoretical model based on Random-Matrix Theory, validated by phase-field simulations, to characterizes the rich emergent dynamics, compositions, and steady-state properties that underlie multi-phase coexistence in fluid mixtures with many randomly interacting components.2. Motivated by puzzles in gene-regulation and nuclear organization, I will propose a role for how liquid-like nuclear condensates can be organized and regulated by the active process of RNA synthesis (transcription) and RNA-protein coacervation. Here, I will describe theory and simulations based on a Landau formalism and recent experimental results from collaborators.Zoom link: https://harvard.zoom.us/j/96657833341 - 17September 17, 2021
CMSA Quantum Matter in Mathematics & Physics Seminar: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction
In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.
—–
Subscribe to Harvard CMSA seminar videos (more to be uploaded):
https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww - 18September 18, 2021No events