BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Roland Speicher (Saarbrucken) DTSTART:20200512T150000Z DTEND:20200512T160000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/1 DESCRIPTION:Title: Random matrices and their limits\nby Roland Speicher (Saar brucken) as part of Wales MPPM Mathematical Physics\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Makoto Yamashita (Oslo) DTSTART:20200519T153000Z DTEND:20200519T163000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/2 DESCRIPTION:Title: Categorical quantization of symmetric spaces and reflection eq uation\nby Makoto Yamashita (Oslo) as part of Wales MPPM Mathematical Physics\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Tobias Osborne (Hannover) DTSTART:20200526T153000Z DTEND:20200526T163000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/3 DESCRIPTION:Title: The search for a Haagerup CFT: a microscopic approach\nby Tobias Osborne (Hannover) as part of Wales MPPM Mathematical Physics\n\nAb stract: TBA\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Hollands (Leipzig) DTSTART:20200602T153000Z DTEND:20200602T163000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/4 DESCRIPTION:Title: State recovery\nby Stefan Hollands (Leipzig) as part of Wa les MPPM Mathematical Physics\n\n\nAbstract\nPhysical operations on quantu m states correspond to channels\, i.e. completely positive maps.\nSuch ope rations are typically not invertible. Given that a state having gone throu gh a channel cannot be completely recovered\, it is an important question -- both theoretically but also\nfor practical purposes such as quantum err or correction -- under what circumstances the state can perhaps be recover ed with a high fidelity\, and how. As is well known\, channels may only re duce the relative entropy between the given state and some reference state \, a fact expressed by the famous "data processing inequality". In this ta lk\, I present a strengthened version of this inequality for arbitrary ch annels on v. Neumann algebras and explain how this inequality characterize s the efficiency of state recovery.(Based on joint work with T. Faulkner. )\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhengfeng Ji (UTS Sydney) DTSTART:20200609T100000Z DTEND:20200609T110000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/5 DESCRIPTION:Title: A complexity-theoretic solution to Connes' Embedding Problem\nby Zhengfeng Ji (UTS Sydney) as part of Wales MPPM Mathematical Physic s\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilijas Farah (York\, Ontario) DTSTART:20200616T153000Z DTEND:20200616T163000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/6 DESCRIPTION:Title: Recent applications of set theory to operator algebras\nby Ilijas Farah (York\, Ontario) as part of Wales MPPM Mathematical Physics\ n\n\nAbstract\nCertain questions in the theory of operator algebras have b een recently resolved using set theory. In this talk I’ll concentrate on representation theory of simple C*-algebras and on the structure of the C alkin algebra as well as the other coronas (i.e.\, outer multiplier algebr as) of separable\, non-unital\, C*-algebras. No previous knowledge of set theory or logic will be assumed.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Gus Lehrer (Sydney U) DTSTART:20200623T090000Z DTEND:20200623T100000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/7 DESCRIPTION:Title: The second fundamental theorem of invariant theory for the ort hosymplectic and periplectic groups\nby Gus Lehrer (Sydney U) as part of Wales MPPM Mathematical Physics\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Constantin Teleman (Berkeley) DTSTART:20200630T153000Z DTEND:20200630T163000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/8 DESCRIPTION:Title: Go and No-Go in Chern-Simons theory\nby Constantin Teleman (Berkeley) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nThe 3-dimensional Chern-Simons theory for a compact Lie group G is an intrigui ng topological field theory which admits a distinguished 2D boundary theor y\, the conformal WZW model. No topological boundary theories are known ex cept in very special cases. (“Gapped” and “ungapped” are sometimes used in lieu of conformal and topological.) Recently\, Dan Freed and myse lf showed that\, in the setting of fully extended TQFTs\, no such boundary theories can exist\, unless the Chern-Simons theory is equivalent to a c ombinatorial state-sum theory (of Turaev-Viro type). After recalling that “no-go” result\, I will outline its logical development into a “go ” theorem\, which constructs a universal target for Chern-Simons theorie s (and more general Reshetikhin-Turaev ones) in which they are all generat ed by an object attached to a point\, whose Drinfeld center is the relevan t modular tensor category.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/8/ END:VEVENT BEGIN:VEVENT SUMMARY:James Tener (ANU\, Canberra) DTSTART:20200707T090000Z DTEND:20200707T100000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/9 DESCRIPTION:Title: Thin cobordisms and operator algebras in conformal field theor y\nby James Tener (ANU\, Canberra) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nThe mathematics of conformal field theory means dif ferent things to different people. The three most common ways of studying 2d chiral conformal field theories are i) vertex aglebras\, ii) nets of op erator algebras\, and iii) geometric field theories which assign invariant s to complex cobordisms. In this talk I will present an extension of the n otion of geometric field theory in which the Riemann `surfaces’ are allo wed to have incoming and outgoing boundary overlap. I will also discuss ho w these `surfaces’ give new realizations of nets of observables\, and ho w these ideas have been applied to answer operator algebraic questions in conformal field theory.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Mike Hartglass (Santa Clara) DTSTART:20200714T153000Z DTEND:20200714T163000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/10 DESCRIPTION:Title: Realizations of Rigid C*-tensor categories as bimodules over GJS C*-algebras\nby Mike Hartglass (Santa Clara) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nGiven a countably generated rigid C*- tensor category\, C\, I will construct a separable\, simple\, unital C*-al gebra B with unique trace\, along with a fully faithful functor F from C i nto the finitely-generated projective modules over B. This is joint work with Roberto Hernandez Palomares.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Charlesworth (Berkeley) DTSTART:20200908T153000Z DTEND:20200908T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/11 DESCRIPTION:Title: Free Stein Dimension\nby Ian Charlesworth (Berkeley) as p art of Wales MPPM Mathematical Physics\n\n\nAbstract\nRegularity questions in free probability ask what can be learned about a tracial von Neumann a lgebra from probabilistic-flavoured qualities of a set of generators. Broa dly speaking there are two approaches -- one based in microstates\, one in free derivations -- which with the failure of Connes Embedding are now kn own to be distinct. The non-microstates approach is not obstructed by non- embeddable variables\, but can be more difficult to work with for other re asons. I will speak on recent work with Brent Nelson\, where we introduce a quantity called the free Stein dimension\, which measures how readily de rivations may be defined on a collection of variables. I will spend some t ime placing it in the context of other non-microstates quantities\, and sk etch a proof of the exciting fact that free Stein dimension is a *-algebra invariant.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Barry Simon (Cal Tech) DTSTART:20200915T153000Z DTEND:20200915T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/12 DESCRIPTION:Title: The Tale of a Wrong Conjecture: Borg’s Theorem for Periodic Jacobi Matrices on Trees\nby Barry Simon (Cal Tech) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nI will begin by reviewing work on removal of eigenvalue degeneracy and its relevance to gap splitting. I’ ll next discuss Borg’s theorem. I’ll then describe a framework for dis cussing periodic Jacobi matrices on trees and possible versions of Borg’ s theorem and a recent note that there are counterexamples. Finally\, I’ ll discuss possible modified conjectures. This includes joint work with Ni r Avni and Jonathan Breuer.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Neshveyev (Oslo) DTSTART:20200922T153000Z DTEND:20200922T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/13 DESCRIPTION:Title: Dual cocycles and quantization of locally compact groups\ nby Sergey Neshveyev (Oslo) as part of Wales MPPM Mathematical Physics\n\n \nAbstract\nAlthough the problem of quantization of Lie bialgebras in the purely algebraic (formal) setting was solved in full generality in the 199 0s by Etingof and Kazhdan\, the list of noncompact Lie bialgebras admittin g a quantization in the analytic (operator algebraic) setting is still qui te short. In my talk I will review the history of the problem and its conn ection to classification of group actions on von Neumann algebras. I will then consider a particular class of semidirect products. The simplest exam ple in this class is the ax+b group over the reals. An operator algebraic quantum analogue of this group was defined by Baaj and Skandalis\, and as an application of a general theory it is now possible to show that it is o btained by the dual cocycle twisting from the von Neumann algebra of the a x+b group. (Based on a joint work with Pierre Bieliavsky\, Victor Gayral and Lars Tuset.)\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Ezra Getzler (Northwestern) DTSTART:20200929T153000Z DTEND:20200929T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/14 DESCRIPTION:Title: Lie n-groupoids\nby Ezra Getzler (Northwestern) as part o f Wales MPPM Mathematical Physics\n\n\nAbstract\nI’ll discuss the defini tion and some examples of Banach Lie groupoids. This is joint work with Ka i Behrend. The basic example is a generalization of the Lie group GL(A) of invertible elements of a Banach algebra\, but for differential graded Ban ach algebras\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Jon Keating (Oxford) DTSTART:20201006T153000Z DTEND:20201006T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/15 DESCRIPTION:Title: Joint Moments of Characteristic Polynomials of Random Unitary Matrices Abstact:\nby Jon Keating (Oxford) as part of Wales MPPM Mat hematical Physics\n\n\nAbstract\nI will review what is known and not known about the joint moments of the characteristic polynomials of random unita ry matrices and their derivatives. I will then explain some recent results which relate the joint moments to an interesting class of measures\, know n as Hua-Pickrell measures. This leads to the proof of a conjecture\, due to Chris Hughes in 2000\, concerning the asymptotics of the joint moments\ , as well as establishing a connection between the measures in question an d one of the Painlevé equations. This is joint work with Theo Assiotis a nd Jon Warren.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Inna Entova-Aizenbud (Ben Gurion) DTSTART:20201013T153000Z DTEND:20201013T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/16 DESCRIPTION:Title: Jacobson-Morozov Lemma for Lie superalgebras using semisimpli fication\nby Inna Entova-Aizenbud (Ben Gurion) as part of Wales MPPM M athematical Physics\n\n\nAbstract\nI will present a generalization of the Jacobson-Morozov Lemma for quasi-reductive algebraic supergroups (respecti vely\, Lie superalgebras)\, based on the idea of semisimplification of ten sor categories\, which will be explained during the talk. This is a joint project with V. Serganova.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Narutaka Ozawa (RIMS Kyoto) DTSTART:20201020T100000Z DTEND:20201020T120000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/17 DESCRIPTION:Title: An entropic proof of cutoff on Ramanujan graphs\nby Narut aka Ozawa (RIMS Kyoto) as part of Wales MPPM Mathematical Physics\n\n\nAbs tract\nIt is recently proved by Lubetzky and Peres that the simple random walk on a Ramanujan graph exhibits a cutoff phenomenon\, that is to say\, the total variation distance of the random walk distribution from the unif orm distribution drops abruptly from near 1 to near 0. I will talk about a very simple proof based on functional analysis and entropic consideration .\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Lai-Sang Young (Courant NYU) DTSTART:20201027T163000Z DTEND:20201027T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/18 DESCRIPTION:Title: Observable events and typical trajectories in finite and inf inite dimensional dynamical systems\nby Lai-Sang Young (Courant NYU) a s part of Wales MPPM Mathematical Physics\n\n\nAbstract\nSome of the words in the title are obviously subject to interpretation. For dynamical syste ms on finite dimensional spaces\, one often equates observable events with positive Lebesgue measure sets\, and invariant measures that reflect the large-time behaviors of positive Lebesgue measure sets of initial conditio ns are considered to be of special importance. I will begin by reviewing t hese concepts for general dynamical systems\, describing a simple dynamica l picture that one might hope to be true. Reality is a little messier\, bu t a small amount of random noise will bring this picture about. In the sec ond part of my talk I will consider infinite dimensional systems such as s emi-flows arising from dissipative evolutionary PDEs\, and discuss the ext ent to which the ideas above can be generalized to infinite \ndimensions\, proposing a notion of ``typical solutions".\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Theo Johnson-Freyd (Dalhousie and Perimeter) DTSTART:20201110T163000Z DTEND:20201110T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/19 DESCRIPTION:Title: Pseudounitary slightly degenerate braided fusion categories a dmit minimal modular extensions\nby Theo Johnson-Freyd (Dalhousie and Perimeter) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nA bra ided fusion category is "slightly degenerate" if its Muger centre is a cop y of SVec: they arise as the line operators of 3d spin-TFTs. It is a longs tanding conjecture that any such braided fusion category admits a "minimal modular extension"\, i.e. an index-2 extension to a nondegenerate braided fusion category. I will outline a proof\, which is joint work in progress with David Reutter\, of this conjecture in the pseudounitary case. The pr oof involves traveling into four\, and briefly five\, dimensions.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Cris Negron (U of North Carolina) DTSTART:20201117T163000Z DTEND:20201117T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/20 DESCRIPTION:Title: Quantum groups at even roots of unity and their corresponding vertex algebras\nby Cris Negron (U of North Carolina) as part of Wale s MPPM Mathematical Physics\n\n\nAbstract\nI will discuss quantum groups a t even roots of unity and their corresponding logarithmic CFTs/VOAs. I wi ll focus on quantum SL(2) and the triplet vertex operator algebra. Here t here is a conjectured (ribbon tensor) equivalence between the category of representations for small quantum SL(2)\, and the category of representati ons for the triplet algebra. In the talk I will explain how certain pheno mena on the VOA side of this conjecture are mirrored on the quantum group side\, and how such mirrored phenomena might inform how we approach the co njectured equivalence\, and related equivalences in ``higher rank".\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Ralf Meyer (Gottingen) DTSTART:20201201T163000Z DTEND:20201201T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/21 DESCRIPTION:Title: Coarse geometry and topological insulators\nby Ralf Meyer (Gottingen) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nI e xplain that topological materials with no restriction on disorder may be m odelled by the Roe C*-algebra of the Euclidean space of appropriate dimens ion. The K-theory of this observable algebra gives exactly the strong top ological phases. In this picture\, the bulk-boundary correspondence is re lated to the coarse Mayer-Vietoris sequence. Explicit formulas for the bo undary map in van Daele's K-theory will be deduced from the naturality of the boundary map. In the end\, I would like to discuss how the descriptio n of strong topological phases could be extended to interacting field theo ries. Here the description through the Roe C*-algebra indicates a possibl e way. Namely\, the position observables already generate the Hilbert spa ce representation of the Roe C*-algebra. A Hamiltonian gives a class in t he K-theory of the Roe C*-algebra provided it has a spectral gap\, is loca lly compact\, and norm-continuous for the R^d-action generated by the posi tion observables.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Philippe Di Francesco (U of Illinois At Urbana-Champaign and IPhT Saclay) DTSTART:20201124T163000Z DTEND:20201124T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/22 DESCRIPTION:Title: Triangular Ice: Combinatorics and Limit Shapes\nby Philip pe Di Francesco (U of Illinois At Urbana-Champaign and IPhT Saclay) as par t of Wales MPPM Mathematical Physics\n\n\nAbstract\nWe consider the triang ular lattice version of the two-dimensional ice model with suitable bounda ry conditions\, leading to an integrable 20 Vertex model. Configurations g ive rise to generalizations of Alternating Sign Matrices\, which we call A lternating Phase Matrices (APM). After reviewing a few facts on the square lattice version and the role of integrability\, we compute the number of APM of any given size in the form of a determinant\, which turns out to ma tch the number of quarter-turn symmetric domino tilings of a quasi-Aztec s quare with a central cross-shaped hole. We also present conjectures for tr iangular Ice with other types of boundary conditions\, and results on the limit shape of large APM\, obtained by applying the so-called "Tangent Met hod".\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Thomas (Imperial) DTSTART:20201103T163000Z DTEND:20201103T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/23 DESCRIPTION:Title: Counting sheaves on Calabi-Yau 4-folds\nby Richard Thomas (Imperial) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nI wi ll outline\, in a down-to-earth way\, how invariants are extracted from mo duli spaces in modern enumerative algebraic geometry. The key tool is some thing called a “virtual cycle”\, which can be understood as some kind of “localised Euler class”. We will see this works for 3 complex dimen sional Calabi-Yau manifolds\, but not for 4-folds. Then I will explain a f ix using “localised square root Euler classes for special orthogonal bun dles”. Joint work with Jeongseok Oh (KIAS).\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Bourne (Tohoku U) DTSTART:20201208T110000Z DTEND:20201208T130000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/24 DESCRIPTION:Title: Gapped ground states and symmetry protected topological (SPT) phases of infinite fermion chains\nby Chris Bourne (Tohoku U) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nGapped ground states ha ve attracted much interest from physicists and mathematicians as a means t o characterise physical effects that are described by topological invarian ts and therefore stable under small perturbations. In this talk I will rev iew the analytic/operator algebraic approach to gapped ground states\, whi ch allows us to work in the thermodynamic limit directly. I will then show how the split property allows us to define topological indices to pure ga pped 1D ground states with an on-site finite group symmetry. Time permitti ng\, I will also compare to other methods to study SPT phases such as tens or networks and (invertible) TQFT. This is joint work with Yoshiko Ogata ( Univ. Tokyo)\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Feng Xu (UC Riverside) DTSTART:20201215T163000Z DTEND:20201215T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/25 DESCRIPTION:Title: Rigorous results about relative entropy in QFT\nby Feng Xu (UC Riverside) as part of Wales MPPM Mathematical Physics\n\n\nAbstract \nWe will present some rigorous results about relative entropy in QFT\, m otivated in part by recent physicists work which however depends on heuri stic arguments such as introducing cut off and using path integrals. In th e particular case of CFT\, we will discuss interesting relations between r elative entropy\, central charge and global dimension of conformal net.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudia Scheimbauer (TU Munich) DTSTART:20210126T163000Z DTEND:20210126T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/26 DESCRIPTION:Title: The AKSZ construction as a fully extended topological field t heory\nby Claudia Scheimbauer (TU Munich) as part of Wales MPPM Mathem atical Physics\n\n\nAbstract\nClassical Poincaré-Lefschetz duality is a s tarting point of understanding what an orientation on a derived stack give n by a homotopy type of a cobordism M is. If furthermore we have an (n-)sy mplectic "target" X\, we obtain a (shifted) symplectic on Map(M\,X) which is given by pulling back along an evaluation and then integrating. This ex plains the Atiyah-Bott symplectic form on G-local systems\, arising from t he Killing form on the Lie algebra of a reductive group G\, via derived s ymplectic geometry in the sense of Pantev-Toen-Vaquié-Vezzosi. In this ta lk I will sketch these ideas and explain how this leads to a fully extende d oriented topological field theory with values in a suitable higher categ ory of Lagrangians\, explaining the difficulties with coherence in definin g such a functor. In essence\, the difficulty with coherence stems from in tegration of differential forms not being functorial for cobordisms on the nose\, but only up to homotopy. In mathematical physics\, this TFT is a r einterpretation/analog of the classical AKSZ construction for certain $\\s igma$-models and describes "semi-classical TFTs”. This is joint work wit h Damien Calaque and Rune Haugseng and fully extends a construction by the former.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Cherednik (U North Carolina\, Chapel Hill) DTSTART:20210202T163000Z DTEND:20210202T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/27 DESCRIPTION:Title: Riemann hypothesis for plane curve singularities\nby Ivan Cherednik (U North Carolina\, Chapel Hill) as part of Wales MPPM Mathemat ical Physics\n\n\nAbstract\nWe will begin with a mini-review of the classi cal theories of\nzeta-functions\, and then switch to the zeta and L-functi ons\nof plane curve singularities\, conjecturally coinciding with the\nmot ivic super-polynomials\, defined in terms of compactified\nJacobians of th ese singularities. The focus is on the functional\nequation\, matching the DAHA super-duality and\, presumably\,\nthe physics S-duality in M-theory. DAHA provides here powerful\noperator methods\, closely related to refine d Verlinde algebras.\nWe will calculate the DAHA super-polynomial and the motivic\none for trefoil. Generally\, they are expected to coincide with\n the stable Khovanov-Rozansky polynomials of algebraic knots.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Schopieray (PIMS) DTSTART:20210209T163000Z DTEND:20210209T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/28 DESCRIPTION:Title: Number fields and the quantum subgroup problem\nby Andrew Schopieray (PIMS) as part of Wales MPPM Mathematical Physics\n\n\nAbstrac t\nThere was a long-standing conjecture that\, stated very loosely\, there exist finitely-many exceptional quantum subgroups for each of the affine Lie algebras. This conjecture can be understood as a question about commu tative algebra objects in modular tensor categories. It was announced a f ew years ago that this conjecture shall become a theorem\, the proof of wh ich relies on number-theoretic aspects of modular tensor categories includ ing the Galois symmetry of modular data. In this talk\, I will discuss bo th results and future directions of research that have arisen from my own contributions to resolving this conjecture\, including Witt group relation s\, non-pseudounitary fusion rules\, and minimal modular closure conjectur es.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Bin Gui (Rutgers) DTSTART:20210216T163000Z DTEND:20210216T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/29 DESCRIPTION:Title: Categorical extensions of conformal nets\nby Bin Gui (Rut gers) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nWightman Q FT and Haag-Kastler QFT are two major mathematically rigorous axiomatizati ons of quantum field theory. For 2d chiral conformal field theory\, these two are respectively the vertex operator algebra approach (describing the chiral fields) and the conformal net approach (describing bounded observab les on the circle). To construct and understand full and boundary CFT\, an d to investigate the representation tensor categories for chiral CFT\, one also needs charged fields (known as intertwining operators or conformal b locks in the literature of vertex algebras) which map between different re presentations of the chiral fields. In this talk\, I will introduce catego rical extensions of conformal nets as a Haag-Kastler theory for charged fi elds. I will argue that this approach provides a natural framework of desc ribing the locality property for charged fields. I will use Connes fusion (Connes relative tensor product) to motivate the definition.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Mayuko Yamashita (RIMS Kyoto) DTSTART:20210223T110000Z DTEND:20210223T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/30 DESCRIPTION:Title: The classification problem of non-topological invertible QFT ’s and a “physicists-friendly” model for the Anderson duals\nby Mayuko Yamashita (RIMS Kyoto) as part of Wales MPPM Mathematical Physics\n \n\nAbstract\nFreed and Hopkins conjectured that the deformation classes o f non-topological invertible quantum field theories are classified by a ge neralized cohomology theory called the Anderson dual of bordism theories. The main difficulty of this problem lies in the fact that we do not have t he axioms for QFT’s. In this talk\, I will explain the ongoing work to g ive a new approach tothis conjecture. We construct a new\, “physicists-f riendly” model for the Anderson duals.This model is constructed so that it abstracts a certain property of invertible QFT’s which physicists bel ieve to hold in general. I will start from basic motivations for the class ification problem\, report the progress of our work and explain future dir ections. This is the joint work with Yosuke Morita (Kyoto\, math) and Kazu ya Yonekura (Kyushu\, physics).\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Nilanjana Datta (DAMTP Cambrdige) DTSTART:20210302T163000Z DTEND:20210302T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/31 DESCRIPTION:Title: Perfect discrimination of unitary channels and novel quantum speed limits\nby Nilanjana Datta (DAMTP Cambrdige) as part of Wales MP PM Mathematical Physics\n\n\nAbstract\nDiscriminating between unknown obje cts in a given set is a fundamental task in experimental science. Suppose you are given a quantum system which is in one of two given states with eq ual probability. Determining the actual state of the system amounts to doi ng a measurement on it which would allow you to discriminate between the t wo possible states. It is known that unless the two states are mutually or thogonal\, perfect discrimination is possible only if you are given arbitr arily many identical copies of the state.\n\nIn this talk we consider the task of discriminating between quantum channels\, instead of quantum state s. In particular\, we discriminate between a pair of unitary channels acti ng on a quantum system whose underlying Hilbert space is infinite-dimensio nal. We prove that in contrast to state discrimination\, one only needs a finite number of uses of these channels in order to discriminate perfectly between them. Furthermore\, no entanglement is needed in the discriminati on task. The measure of discrimination is given in terms of the energy-con strained diamond norm\, and a key ingredient of the proofs of these result s is a generalization of the Toeplitz-Hausdorff Theorem of convex analysis . Moreover\, we employ our results to study a novel type of quantum speed limits which apply to pairs of quantum evolutions. This work was done joi ntly with Simon Becker (Cambridge)\, Ludovico Lami (Ulm) and Cambyse Rouze (Munich).\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Reinhard Werner (ReinLeibniz Universität\, Hannover) DTSTART:20210309T163000Z DTEND:20210309T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/32 DESCRIPTION:Title: Topological classification of spin chains and quantum walks\nby Reinhard Werner (ReinLeibniz Universität\, Hannover) as part of Wa les MPPM Mathematical Physics\n\n\nAbstract\nI will consider two types of one-dimensional discrete time lattice systems: On the one hand\, there are spin chains\, infinite tensor products of finite quantum systems. With a discrete time evolution automorphism\, they are called quantum cellular au tomata (QCAs). On the other\, there are quantum walks\, direct sums of fin ite quantum systems\, whose one-step dynamics is given by a unitary operat or. In both cases\, the discreteness of time leads to an interesting inter play between unitarity and locality\, which is absent in the continuous ti me (Hamiltonian) analogues. It is measured by an index\, which assumes rat ional values in the QCA case and integers in the walk case. I will illustr ate it by the index theorem for juggling patterns (these are special walks ) and the memory invariant for reversible qubit-stream processors (special QCAs). The geometric features of the lattice are encoded in a "coarse str ucture"\, which will be important for analogues of this theory in higher d imensions. But even in the translation invariant one-dimensional case ther e are different choices\, which I will briefly describe.\n\nI will then co nsider quantum walks with discrete symmetries and a spectral gap condition . No translation invariance and only approximate locality are assumed. In the Hamiltonian case this leads to the so-called tenfold way\, of which I will give a characterization justifying the number ten. In the unitary cas e\, the same assumptions once again lead to more possibilities. Topologica l classification is in terms of an index group\, and requires three indice s: one for the asymptotic behaviour on the left\, one on the right\, and o ne to classify non-gentle perturbations\, i.e.\, local modifications of th e walk that cannot be deformed away.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Cain Edie-Mitchell (Vanderbilt University) DTSTART:20210316T163000Z DTEND:20210316T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/33 DESCRIPTION:Title: Type II quantum subgroups for sl_n\nby Cain Edie-Mitchell (Vanderbilt University) as part of Wales MPPM Mathematical Physics\n\n\nA bstract\nQuantum subgroups are module categories\, which encode the ``high er representation theory'' of the Lie algebras. They appear naturally in m athematical physics\, where they correspond to extensions of the Wess-Zumi no-Witten models. The classification of these quantum subgroups has been a long-standing open problem. The main issue at hand being the possible exi stence of exceptional examples. Despite considerable attention from both p hysicists and mathematicians\, full results are only known for sl_2 and sl _3.\n \nIn this talk I will discuss recent progress in the classification of type II quantum subgroups for sl_n. Our results finish off the classifi cation for n = 4\,5\,6\,7\, and pave the way for higher ranks. In particul ar we discover several exceptional examples.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhengwei Liu (Tsinghua University\, Beijing) DTSTART:20210323T163000Z DTEND:20210323T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/34 DESCRIPTION:Title: Quantum Fourier Analysis\nby Zhengwei Liu (Tsinghua Unive rsity\, Beijing) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\ nQuantum Fourier Analysis is a subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estima tes. This provides interesting tools to investigate phenomena such as quan tum symmetry. In this talk\, we will introduce its background\, developmen t and perspectives\, based on selected examples\, results and applications .\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Yoshiko Ogata (Tokyo U) DTSTART:20210420T100000Z DTEND:20210420T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/35 DESCRIPTION:Title: Classification of gapped ground state phases in quantum spin systems\nby Yoshiko Ogata (Tokyo U) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nI would like to explain about classification of ga pped ground state\nphases in quantum spin systems\, in the operator algebr aic framework of quantum statistical mechanics.The talk consists of two pa rts. The first part is about classification problem of so called SPT (symm etry protected topological) phases. We see that it is classified by group cohomology\, in one and two dimension.In the second part (joint work with Pieter Naaijkens)\, we see that superselection sector is a topological inv ariant.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Riehl (Johns Hopkins) DTSTART:20210427T153000Z DTEND:20210427T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/36 DESCRIPTION:Title: Elements of ∞-Category Theory\nby Emily Riehl (Johns Ho pkins) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nConfusing ly for the uninitiated\, experts in weak infinite-dimensional category the ory make use of different definitions of an ∞-category\, and theorems in the ∞-categorical literature are often proven "analytically"\, in refer ence to the combinatorial specifications of a particular model. In this ta lk\, we present a new point of view on the foundations of ∞-category the ory\, which allows us to develop the basic theory of ∞-categories - adju nctions\, limits and colimits\, co/cartesian fibrations\, and pointwise Ka n extensions - "synthetically" starting from axioms that describe an ∞-c osmos\, the infinite-dimensional category in which ∞-categories live as objects. We demonstrate that the theorems proven in this manner are "model -independent"\, i.e.\, invariant under change of model. Moreover\, there i s a formal language with the feature that any statement about ∞-categori es that is expressible in that language is also invariant under change of model\, regardless of whether it is proven through synthetic or analytic t echniques. This is joint work with Dominic Verity.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuki Arano (Kyoto University) DTSTART:20210504T100000Z DTEND:20210504T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/37 DESCRIPTION:Title: Ergodic theory of affine isometric actions on Hilbert spaces< /a>\nby Yuki Arano (Kyoto University) as part of Wales MPPM Mathematical P hysics\n\n\nAbstract\nI introduce nonsingular actions of groups on probabi lity spaces constructed from affine isometric actions on Hilbert spaces\, which we call the non-singular Gausian action. Then I discuss the ergodici ty and the type determination for groups acting on trees.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Rosenberg (U of Maryland) DTSTART:20210511T153000Z DTEND:20210511T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/39 DESCRIPTION:Title: Gap Labeling and the Noncommutative Bloch Theorem\nby Jon athan Rosenberg (U of Maryland) as part of Wales MPPM Mathematical Physics \n\n\nAbstract\nNoncommutative geometry provides powerful mathematical too ls for studying thephysical properties of non-periodic but still somewhat regular solids. Such materials\, often called “quasi-crystals”\, do o ccur in nature and are based on non-periodic tilings. (These were recogni zed in Schechtman’s 2011 Nobel Prize.) Attempts to predict the Bragg pea ks and spectral properties of such materials led to a program pioneered by Jean Bellissardand pursued by many others\, of studying “gap labeling ”\, predicting spectral gaps based on thedynamics of the tiling. This i s closely related to the Čech cohomology of the “tiling space” andthe K-theory of a certain C*-algebra associated to the tiling. We explain ho w this comes about\,how various people gave false proofs of the “Gap Lab eling Conjecture”\, and how to obtain somenew results. This is joint wo rk with Claude Schochet\, Eric Akkermans\, and Yaroslav Don.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Johannes Kellendonk (JohanneUniversité Claude Bernard Lyon 1) DTSTART:20210525T153000Z DTEND:20210525T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/40 DESCRIPTION:Title: Bragg spectrum and gap-labelling\, a topological approach \nby Johannes Kellendonk (JohanneUniversité Claude Bernard Lyon 1) as par t of Wales MPPM Mathematical Physics\n\n\nAbstract\nA classical result in solid state physics tells us that the gaps in the electronic spectrum of a one dimensional crystal are located at those values for the quasi momentu m k which belong to the Bragg spectrum of the crystal. The result is prove n by perturbation theory. If one labels a gap with the integrated density of states of energies up to that gap one obtains an order preserving map f rom the positive Bragg spectrum to the set of gap labels. \nThe purpose of the talk is to explain a similar map for aperiodic solids which is based on methods from non-commutative topology\, namely we discuss an order pres erving homomorphism between the group of topological Bragg peaks and the g ap labelling group. \nA comparison with work by theoretical physicists fro m the late ‘80s\, which is based on a perturbation expansion of the trac e map for hierarchical systems\, finds disagreement. Not all gaps predicte d by these perturbative expansions are there. $K$-theory provides selectio n rules on the opening of gaps.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Buican (Queen Mary\, London) DTSTART:20210601T153000Z DTEND:20210601T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/41 DESCRIPTION:Title: aXb=c in 2+1D TQFT\nby Matthew Buican (Queen Mary\, Londo n) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nI will discus s fusion rules of the form aXb=c in 2+1D topological quantum field theorie s. Here a\, b\, and c are simple objects of the associated modular tensor categories (MTC). As I will explain\, when a and b have categorical dimens ion larger than one\, such fusion rules imply interesting global constrain ts on the MTC. The simplest possibility is that the MTC factorizes\, but t here are other\, more interesting\, possibilities as well. Some of these l atter possibilities may potentially be relevant for understanding various problems in mathematical physics that I will describe.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Arnaud Brothier (UNSW\, Sydney) DTSTART:20210928T100000Z DTEND:20210928T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/42 DESCRIPTION:Title: Jones' actions: from conformal field theory to Richard Thomps on’s group\nby Arnaud Brothier (UNSW\, Sydney) as part of Wales MPPM Mathematical Physics\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Ostrik (Eugene\, Oregon) DTSTART:20211005T153000Z DTEND:20211005T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/43 DESCRIPTION:Title: Two dimensional topological field theories and partial fracti ons\nby Victor Ostrik (Eugene\, Oregon) as part of Wales MPPM Mathemat ical Physics\n\nAbstract: TBA\n\nbased on joint work with M. Khovanov and Y. Kononov. By evaluating a topological field theory in dimension 2 on sur faces of genus 0\,1\,2 etc we get a sequence. We investigate which sequenc es occur in this way depending on the assumptions on the target category.\ n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Ehud Meir (Aberdeen) DTSTART:20211012T153000Z DTEND:20211012T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/44 DESCRIPTION:Title: Interpolations of monoidal categories by invariant theory \nby Ehud Meir (Aberdeen) as part of Wales MPPM Mathematical Physics\n\n\n Abstract\nIn this talk I will consider algebraic structures such as lie\, Hopf\, and Frobenius algebras. \nI will show that under certain assumption s such structures can be reconstructed from the scalar invariants they def ine. I will then show how one can interpolate the category of representati on of the automorphism groups of the structures by interpolation the invar iants of the algebraic structures. In this way we recover the construction s of Deligne for categories such as Rep(S_t)\, Rep(O_t) and Rep(Sp_t)\, th e constructions of Knop for\nwreath products with S_t\, and GL_t(O_r)\, wh ere O_r is a finite quotient\nof a discrete valuation ring. We will also s how how the TQFT categories recently\nconstructed from a rational function by Khovanov\, Ostrik\, and Kononov arise in this context.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Semeon Artamonov (CRM\, Montreal) DTSTART:20211019T153000Z DTEND:20211019T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/45 DESCRIPTION:Title: Genus two Double Affine Hecke Algebra and its classical limit \nby Semeon Artamonov (CRM\, Montreal) as part of Wales MPPM Mathemati cal Physics\n\n\nAbstract\nWith every surface and reductive group G one ca n associate G-character variety of its fundamental group. When the surface is oriented\, the coordinate ring of G-character variety comes equipped w ith the Goldman Poisson bracket. The quantization of this Poisson algebra is known as G-skein algebra.\n\nIt is known that G-skein algebra of a toru s admits flat one-parameter deformation into spherical subalgebra of Doubl e Affine Hecke Alegrba (sDAHA). In my talk I will define a genus two analo gue of sDAHA for G=SL(2). I will talk about finite-dimensional representat ions of this algebra\, relation to TQFT\, classical limit\, and genus two analogue of Macdonald polynomials.\n\nThis talk is based on joint work wit h Sh.Shakirov.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergei Gukov (Caltech & DIAS\, Dublin) DTSTART:20211026T153000Z DTEND:20211026T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/46 DESCRIPTION:Title: MTCs and TQFTs from 3d Coulomb branches\nby Sergei Gukov (Caltech & DIAS\, Dublin) as part of Wales MPPM Mathematical Physics\n\nAb stract: TBA\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Ioana (UCSD) DTSTART:20211102T163000Z DTEND:20211102T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/47 DESCRIPTION:Title: Almost commuting matrices and stability for product groups\nby Adrian Ioana (UCSD) as part of Wales MPPM Mathematical Physics\n\n\n Abstract\nI will present a result showing that the direct product group $G =\\mathbb F_2\\times\\mathbb F_2$ is not Hilbert-Schmidt stable. This mean s that G admits a sequence of asymptotic homomorphisms (with respect to th e normalized Hilbert-Schmidt norm) which are not perturbations of genuine homomorphisms. While this result concerns unitary matrices\, its proof re lies on techniques and ideas from the theory of von Neumann algebras. I wi ll also explain how this result can be used to settle in the negative a na tural version of an old question of Rosenthal concerning almost commuting matrices. More precisely\, we derive the existence of contraction matrices A\,B such that A almost commutes with B and B* (in the normalized Hilbert -Schmidt norm)\, but there are no matrices A’\,B’ close to A\,B such t hat A’ commutes with B’ and B’*.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Colleen Delaney (Indiana U\, Bloomington) DTSTART:20211109T163000Z DTEND:20211109T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/48 DESCRIPTION:Title: Zesting and Witten-Reshetikhin-Turaev invariants\nby Coll een Delaney (Indiana U\, Bloomington) as part of Wales MPPM Mathematical P hysics\n\n\nAbstract\nI’ll discuss the ribbon zesting construction on pr e-modular categories from a diagrammatic point of view and show that Witte n-Reshetekhin-Turaev invariants of framed knots and links decouple under z esting. As an application I will explain how the Mignard-Schauenburg ``mod ular isotopes” can be understood through zesting.\n\nThis talk is based on joint work with Cesar Galindo\, Julia Plavnik\, Eric Rowell\, and Qing Zhang as well as Sung Kim.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Moritz Weber (Saarland) DTSTART:20211123T163000Z DTEND:20211123T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/49 DESCRIPTION:Title: Easy quantum groups and quantum permutations\nby Moritz W eber (Saarland) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\n Within Woronowicz’s framework of compact quantum groups\, there are natu ral quantum analogs of the symmetric group\, the orthogonal group and the unitary group\, amongst others. They have in common that their representat ion theory may be expressed in terms of diagrams. This has been systematic ally formalized by Banica and Speicher in 2009 within the class of so call ed „easy“ quantum groups. We give an introduction to „easy“ quantu m groups\, their diagrammatic representation theory and we mention some li nks with Deligne’s interpolation categories. Moreover\, we highlight the role of quantum permutations within the theory of quantum automorphism gr oups of graphs. This also links with nonlocal games in quantum information theory\, as we will point out.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacob Bridgeman (Perimeter) DTSTART:20211130T163000Z DTEND:20211130T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/50 DESCRIPTION:Title: Enriched topological codes\nby Jacob Bridgeman (Perimeter ) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nTopological ph ases are a promising substrate for quantum computing due to their inherent error resistance. Unfortunately\, there seems to be a tradeoff between ho w easily the codes can be realized in the lab\, and whether a universal se t of gates can be implemented. Including defects into the code can be used to boost the gateset. We use tube algebras to understand the properties o f defects\, and hopefully which gates can be implemented.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Gwyn Bellamy (Glasgow) DTSTART:20211207T163000Z DTEND:20211207T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/51 DESCRIPTION:Title: Invariant holonomic systems for symmetric spaces\nby Gwyn Bellamy (Glasgow) as part of Wales MPPM Mathematical Physics\n\n\nAbstrac t\nIf G is a reductive (connected\, complex) Lie group with Lie algebra g\ , then Hotta-Kashiwara introduced a certain D-module HC on g called the Ha rish-Chandra D-module. This is precisely the module whose distributional s olutions are the invariant eigen-distributions appearing in character theo ry for real reductive Lie groups. A key result by Hotta-Kashiwara is that HC is semi-simple with simple summands in bijection with the irreducible r epresentations of the Weyl group (the algebraic Springer correspondence). In this talk I'll describe a natural generalization of HC to a D-module on the tangent space of a symmetric space. I'll explain the extent to which Hotta-Kashiwara's results generalise to this setting. This is based on joi nt work with Levasseur\, Nevins and Stafford\; I won't assume any prior kn owledge of D-modules.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/51/ END:VEVENT BEGIN:VEVENT SUMMARY:George Willis (Newcastle\, NSW) DTSTART:20211116T110000Z DTEND:20211116T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/52 DESCRIPTION:Title: Flat groups of automorphisms of totally disconnected locally compact groups.\nby George Willis (Newcastle\, NSW) as part of Wales M PPM Mathematical Physics\n\n\nAbstract\nFlat groups of automorphisms are f eatures of the structure of totally disconnected locally compact (t.d.l.c. ) groups that roughly correspond to Cartan subgroups in Lie and algebraic groups. \nThe group $\\mathcal{H}$ of automorphisms of the t.d.l.c. group $G$ is flat if there is $U\\leq G$ that is minimising for every $\\alpha\\ in\\mathcal{H}$\, and a compact open subgroup $U$ of $G$ is \\emph{minimis ing} for $\\alpha$ if the index $[\\alpha(U) : \\alpha(U)\\cap U]$ is the minimum as $U$ ranges over all compact open subgroups of $G$. \n\nThe stru cture of flat groups and the associated minimising subgroups can be descri bed in some detail and the first part of the talk will summarise this desc ription. A couple of applications will then be outlined. The last part of the talk will describe work in progress that strengthens the correspondenc e with Lie algebra significantly and increases the scope of the structure theorems.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Claus Koestler (Cork) DTSTART:20220201T163000Z DTEND:20220201T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/53 DESCRIPTION:Title: Spreadability and Partial Spreadability\nby Claus Koestle r (Cork) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nDistrib utional symmetries and invariance principles provide deep structural resul ts in classical probability\, also known as de Finetti theorems. I will in troduce to some recent developments in the transfer of these principles to noncommutative probability. \n\nFirst\, I will discuss spreadability of a n infinite sequence of noncommutative random variables. This property is a bout the invariance of distributions when passing from the given sequence to a subsequence. It may be regarded to be the fundamental distributional invariance principle from the viewpoint of algebraic homology as it emerg es via a functor from the semisimplicial category into a category of nonco mmutative probability spaces. \n\nFurthermore\, my talk will address part ial spreadability\, a recently introduced generalization of spreadability. This invariance principle provides a connection between certain represen tations of the Thompson monoid $F^+$ and Markovianity in noncommutative p robability.\n\nFinally\, as time permits\, I will address some open proble ms when applying these two invariance principles to Jones-Temperley-Lieb a lgebras. \n\nThis talk is based on joint work with Gwion Evans\, Rolf Goh m\, Arundhathi Krishnan and Steven Wills. \n\n\nReferences:\n\nD. Gwion Evans\, Rolf Gohm\, Claus Köstler. Semi-cosimplicial objects and spreada bility. Rocky Mountain J. Math. 47 (6) 1839 - 1873\, 2017.\n\nClaus Köst ler\, Arundhathi Krishnan\, Stephen J. Wills. Markovianity and the Thomps on Monoid $F^+$\, arXiv:2009.14811.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Guoliang Yu (Texas A&M) DTSTART:20220208T163000Z DTEND:20220208T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/54 DESCRIPTION:Title: A new index theory for noncompact manifolds and Gromov's comp actness conjecture\nby Guoliang Yu (Texas A&M) as part of Wales MPPM M athematical Physics\n\n\nAbstract\nI will introduce a new index theory for noncompact manifolds based on my joint work with Stanley Chang and Shmuel Weinberger. This index theory encodes dynamics of the fundamental groups at infinity. I will then discuss my recent work with Shmuel Weinberger and Zhizhang Xie answering Gromov's compactness question on scalar curvature using this index theory.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Jesse Peterson (Vanderbilt) DTSTART:20220215T163000Z DTEND:20220215T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/55 DESCRIPTION:Title: Properly proximal von Neumann Algebras\nby Jesse Peterson (Vanderbilt) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nPr operly proximal groups were introduced recently by Boutonnet\, Ioana\, and the speaker\, where they generalized several rigidity results to the sett ing of higher-rank groups. In this talk\, I will describe how the notion o f proper proximality fits naturally in the realm of von Neumann algebras. I will also describe several applications\, including that the group von N eumann algebra of a non-amenable inner-amenable group cannot embed into a free group factor\, which solves a problem of Popa. This is joint work wit h Changying Ding and Srivatsav Kunnawalkam Elayavalli.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandru Chirvasitu (Buffalo) DTSTART:20220222T163000Z DTEND:20220222T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/56 DESCRIPTION:Title: Flavors of rigidity\nby Alexandru Chirvasitu (Buffalo) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nI will discuss a n umber of results which\, though to my knowledge not mutually related in an y direct manner\, nevertheless have a recognizably common flavor: "most" o bjects of such-and-such a type have "few" symmetries. Examples abound\; th e objects in question might be\n\n- finite graphs\, where "most" is interp reted probabilistically and asymptotically as the graphs grow\;\n\n- quant um graphs (i.e. appropriately well-behaved subspaces of matrix algebras)\, where "most" means "along a Zariski-dense subset"\;\n\n- measured metric spaces\, with "most" = "over a residual set in the measured Gromov-Hausdor ff topology"\;\n\n- Riemannian manifolds\, "most" meaning "over an open de nse set in the smooth topology".\n\n"Few symmetries" is also subject to ri ch interpretation: it might mean a trivial automorphism group\, or a quant um-group version thereof\, or that the automorphism group can be prescribe d beforehand.\n\n(partly joint w/ Mateusz Wasilewski)\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Amanda Young (TU Munich) DTSTART:20220301T163000Z DTEND:20220301T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/57 DESCRIPTION:Title: A bulk gap in the presence of edge states for a Haldane pseud opotential\nby Amanda Young (TU Munich) as part of Wales MPPM Mathemat ical Physics\n\n\nAbstract\nIn this talk\, we discuss a recent result on a bulk gap for a truncated Haldane \npseudopotential with maximal half fill ing\, which describes a strongly correlated system of spinless bosons in a cylinder geometry. For this Hamiltonian with either open or periodic boun dary conditions\, we prove a spectral gap above the highly degenerate grou nd-state space which is uniform in the volume and particle number. Our pro ofs rely on identifying invariant subspaces to which we apply gap-estimate methods previously developed only for quantum spin Hamiltonians. In the c ase of open boundary conditions\, the lower bound on the spectral gap accu rately reflects the presence of edge states\, which do not persist into th e bulk. Customizing the gap technique to the invariant subspace\, we avoid the edge states and establish a more precise estimate on the bulk gap in the case of periodic boundary conditions. The same approach can also be ap plied to prove a bulk gap for the analogously truncated 1/3-filled Haldane pseudopotential for the fractional quantum Hall effect. Based off joint w ork with S. Warzel.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Elizabeth Gillaspy (Montana) DTSTART:20220315T163000Z DTEND:20220315T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/58 DESCRIPTION:Title: K-theory for real k-graph C*-algebras\nby Elizabeth Gilla spy (Montana) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nPu rely infinite simple real C*-algebras\, like their complex counterparts\, are classified by their K-theory. Indeed\, there are purely infinite simp le real C*-algebras (e.g. the exotic Cuntz algebra E_n) whose existence is only known thanks to K-theory computations. Our long-term goal\, in this joint research project with Jeff Boersema\, is to construct more concrete models for such C*-algebras. We begin by showing how k-graphs\, or highe r-rank graphs (which are a higher-dimensional generalization of directed g raphs)\, can give rise to purely infinite simple real C*-algebras. To eva luate whether this class of real k-graph C*-algebras includes E_n\, we nee d to compute the K-theory of real k-graph C*-algebras. To that end\, we a dapt the spectral sequence studied by D.G. Evans\, which converges to the K-theory of a complex k-graph C*-algebra\, to the setting of real C*-algeb ras. Using this spectral sequence\, we compute K-theory for several exampl es of real k-graph C*-algebras. \nThis is joint work with Jeff Boersema.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/58/ END:VEVENT BEGIN:VEVENT SUMMARY:David Reutter (Bonn) DTSTART:20220308T163000Z DTEND:20220308T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/59 DESCRIPTION:Title: Fusion 2-categories\, their Drinfeld centers\, and the minima l modular extension conjecture\nby David Reutter (Bonn) as part of Wal es MPPM Mathematical Physics\n\n\nAbstract\nA modular tensor category is a ribbon category without any non-trivial transparent object\, while a supe r-modular category is a ribbon category with a single transparent fermion. In this talk\, I will sketch a proof of the "minimal modular extension co njecture" stating that any super-modular category admits an index-2 extens ion to a modular category. Along the way\, I will introduce various key p layers of this proof\, such as fusion 2-categories and their Drinfeld cent ers. This is based on arXiv:2105.15167 and is joint work with Theo Johnson -Freyd.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexis Virelizier (Lille) DTSTART:20220322T163000Z DTEND:20220322T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/60 DESCRIPTION:Title: State sum invariants of homotopy classes of maps\nby Alex is Virelizier (Lille) as part of Wales MPPM Mathematical Physics\n\n\nAbst ract\nHomotopy quantum field theories (HQFTs) generalize topological quant um field theories (TQFTs) by replacing manifolds by maps from manifolds to a fixed target space X. In particular\, such an HQFT associates a scalar invariant under homotopies to each map from a closed manifold to X. In thi s talk\, I will explain how to generalize the state sum Turaev-Viro-Barett -Westburry TQFT to an HQFT with target X in the following two cases. First when X is a 1-type using fusion categories graded by a group (joint work with Vladimir Turaev). Second when X is a 2-type using fusion categories g raded by a crossed module (joint work with Kursat Sozer).\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Bethany Marsh (Leeds) DTSTART:20220510T153000Z DTEND:20220510T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/61 DESCRIPTION:Title: An introduction to tau-exceptional sequences\nby Bethany Marsh (Leeds) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nJo int work with Aslak Bakke Buan (NTNU).\n \nWe introduce the notion of a ta u-exceptional sequence for a finite dimensional algebra\, which can be reg arded as the generalisation of a classical exceptional sequence considered in the hereditary case. The new sequences behave well for both non-heredi tary and hereditary algebras. The work is motivated by the signed exceptio nal sequences introduced\, in the hereditary case\, by Igusa-Torodov\, and by tau-tilting theory.\n \nWe also introduce a notion of a signed tau-exc eptional sequence and show that there is a bijection between the set of co mplete signed tau-exceptional sequences and ordered basic support tau-tilt ing objects.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamie Vicary (Cambridge) DTSTART:20220517T153000Z DTEND:20220517T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/62 DESCRIPTION:Title: HIGHER CATEGORIES AND QUANTUM COMPUTATION\nby Jamie Vicar y (Cambridge) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nI will show how some fundamental computational processes\, including\nencryp ted communication and quantum teleportation\, can be defined in\nterms of the higher representation theory of defects between 2d\ntopological cobord isms\, giving insight into fundamental questions in\nclassical and quantum computation. Everything will be explained from\nfirst principles\, with l ots of pictures!\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannes Thiel (Kiel) DTSTART:20220607T153000Z DTEND:20220607T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/63 DESCRIPTION:Title: Are C*-algebras determined by their linear and orthogonality structure?\nby Hannes Thiel (Kiel) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nIt is well-known that every C*-algebra is determine d by its linear and\nmultiplicative structure: Two C*-algebras are *-isomo rphic if and only\nif they admit a multiplicative\, linear bijection.\n\nW e study if instead of the whole multiplicative structure it suffices to\nr ecord when two elements have zero product. While it is not clear if\nevery C*-algebra is determined this way\, we obtain many positive\nresults. In particular\, two unital\, simple C*-algebras are *-isomorphic\nif and only if they admit a linear bijection that preserves zero products.\n\nThis is joint work with Eusebio Gardella.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/63/ END:VEVENT BEGIN:VEVENT SUMMARY:George Elliott (Toronto) DTSTART:20220531T153000Z DTEND:20220531T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/64 DESCRIPTION:Title: Classification of C*-algebras - simple vs. non-simple\nby George Elliott (Toronto) as part of Wales MPPM Mathematical Physics\n\n\n Abstract\n\n

 Well-behaved simple C*-algebras (ver y simple axioms)

\n\n\n\n

have now been classified. This now leaves the less well

\n\n\n\n

behaved simple case (some evidence! )\, and the non-simple

\n\n\n\n\n\n

already a number of results in the well-behaved non-simple

\n\n\n\n

case.

\n\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Christopher Schafhauser (Lincoln\, Nebraska) DTSTART:20221004T153000Z DTEND:20221004T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/65 DESCRIPTION:Title: Subalgebras of simple AF-algebras\nby Christopher Schafha user (Lincoln\, Nebraska) as part of Wales MPPM Mathematical Physics\n\n\n Abstract\nA long-standing open question\, formalized by Blackadar and Kirc hberg in the mid ‘90s\, asks for an abstract characterization of C*-suba lgebras of AF-algebras. I will discuss some recent progress on this quest ion: every separable\, exact C*-algebra which satisfies the UCT and admits a faithful\, amenable trace embeds into an AF-algebra. Moreover\, the AF -algebra may be chosen to be simple and unital with unique trace and the e mbedding may be taken to be trace-preserving. Modulo the UCT\, this chara cterizes C*-subalgebras of simple\, unital AF-algebras. As an application \, for any countable\, discrete\, amenable group G\, the reduced C*-algebr a of G embeds into a UHF-algebra. I'll also discuss how these techniques have played a role in a new proof to the classification theorem of separab le\, simple\, nuclear\, Z-stable\, UCT C*-algebras\, which is based on joi nt work with Jos\\'e Carri\\'on\, James Gabe\, Aaron Tikuisis\, and Stuart White.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/65/ END:VEVENT BEGIN:VEVENT SUMMARY:William Slofstra (Waterloo) DTSTART:20221101T163000Z DTEND:20221101T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/66 DESCRIPTION:Title: Bell inequalities and decision problems in C*-algebras\nb y William Slofstra (Waterloo) as part of Wales MPPM Mathematical Physics\n \n\nAbstract\nBell inequalities have been in the news lately with the rece nt physics Nobel prize. On the mathematics side\, given a Bell inequality\ , we'd like to be able to determine the maximum possible violation allowed in quantum mechanics. This simple problem has led to a lot of development s in the last few years. In particular\, Ji\, Natarajan\, Vidick\, Wright\ , and Yuen have shown that it's impossible to calculate this violation eve n approximately\, thereby resolving the Connes embedding problem in operat or algebras. In this talk\, I'll give an overview of these developments\, starting with physics\, but with the aim of showing that there are lots of other interesting decision problems in operator algebras. I'll include wo rk with Honghao Fu and Carl Miller on the membership problem for quantum c orrelations\, and work in progress with Arthur Mehta and Yuming Zhao on de ciding positivity.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabor Szabo (KU Leueven) DTSTART:20221108T163000Z DTEND:20221108T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/67 DESCRIPTION:Title: The dynamical Kirchberg-Phillips theorem\nby Gabor Szabo (KU Leueven) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nIn this talk I will present the main results of a joint work with James Gabe: Given a countable discrete group G\, two amenable and outer G-actions on stable Kirchberg algebras are cocycle conjugate precisely when they are eq uivariantly KK-equivalent. In fact we have a suitable version of such a th eorem for actions of locally compact groups. After discussing some of the core concepts\, I will state the classification results and\, depending on the available time\, discuss some interesting corollaries.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Tatiana Gateva-Ivanova (American University in Bulgaria) DTSTART:20221115T163000Z DTEND:20221115T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/68 DESCRIPTION:Title: Set-theoretic solutions of the Yang-Baxter equation and their quadratic algebras\nby Tatiana Gateva-Ivanova (American University in Bulgaria) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nSet-t heoretic solutions of the Yang--Baxter equation (YBE) form a meeting-groun d\nof mathematical physics\, algebra and combinatorics. Such a solution $( X\,r)$\nconsists of a non-empty set $X$\nand a bijective map $r:X\\times X \\to X\\times X$ which satisfies the braid\nrelation\n\\[\nr^{12}r^{23}r^{ 12} = r^{23}r^{12}r^{23}\n\\]\nin $X\\times X\\times X$\, where $r^{12}=r\ \times id_X\,\\\;\\\; r^{23}= id_X\\times r$.\nIn this case $(X\,r)$ is c alled \\emph{a braided set}.\nA braided set $(X\,r)$ with $r$ involutive is called a\nsymmetric set.\n\n\n\nSet theoretic solutions extend to sp ecial linear\n solutions of YBE\, but more important than this is that set -theoretic\nsolutions lead to their own remarkable algebraic and combinato ric\nstructures\, only somewhat analogous to quantum group\nconstructions. They also lead to\n a great deal of combinatorics\, group action on $X$\ , \nmatched pairs of groups\, matched pairs of monoids\, braided groups an d braided monoids\;\nsemigroups of I type with a structure of distributive lattice\;\nquadratic algebras with very nice\n algebraic and homological properties such as being:\n(i) Artin-Schelter\n regular algebras\;\n(ii) K oszul algebras\;\n(iii) Noetherian domains\nwith a $\\textbf{k}$-basis of Poincar\\'{e}-Birkhoff-Witt type\;\n(iv)\nwith good computational properti es -the theory of\nnoncommutative Groebner bases is applicable.\n\n\n\nAss ociated to each set-theoretic solution are several algebraic constructions :\n the braided group $G(X\,r)$\, the braided monoid $S(X\,r)\,$ the quadr atic $\\textbf{k}$ algebra $A(\\textbf{k}\, X\, r) \\cong\n\\textbf{k} S(X \,r)$ over a field $\\textbf{k}$ called \\emph{an Yang-Baxter algebra}. Ea ch of these structures is generated by $X$ and has quadratic relations $xy =\\cdot r(x\,y)$\,\nwhere "$\\cdot$" denotes product in the free monoid\, resp. free group.\n\nIn this talk we shall discuss \\emph{the purely\nma thematical theory} of the Yang-Baxter algebras $A(\\textbf{k}\, X\, r)$\, their remarkable algebraic properties and some applications\nto noncommut ative algebraic geometry- Artin-Schelter regularity\, analogues of Verones e subalgebras\, and Segre products\, Veronese morphisms and Segre morphi sms for Yang-Baxter algebras.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Gregory Moore (Rutgers) DTSTART:20221122T163000Z DTEND:20221122T180000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/69 DESCRIPTION:Title: Summing over bordisms in TQFT\nby Gregory Moore (Rutgers) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nI will review t he contents of the paper I wrote with Anindya Banerjee 2201.00903\, \nincl uding a few updates. We consider a new construction in TQFT which was moti vated by recent developments in the quantum gravity community. Specificall y\, we aim to give mathematical precision to a model proposed by D. Marolf and H. Maxfield 2002.08950. Given a TQFT one can consider - formally - t he sum over all the amplitudes associated to all bordisms between fixed in going and outgoing spatial slices. We discuss when this construction makes sense and a curious splitting property satisfied by the total amplitude. The discussion of the splitting property has been significantly improved b y an important remark by Daniel Friedan.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Palle Jorgensen (Iowa) DTSTART:20221011T153000Z DTEND:20221011T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/70 DESCRIPTION:Title: Reflection positivity\nby Palle Jorgensen (Iowa) as part of Wales MPPM Mathematical Physics\n\n\nAbstract\nThe talk aims to extend tools from reflection positivity (RP) to non-commutative harmonic analysis \, spectral theory\, and new duality theory for unitary representations of Lie groups.\n\nIn its original form\, reflection positivity (RP)\, also r eferred to as Osterwalder-Schrader positivity\, came to serve as a crucial link between problems in quantum physics and in mathematics. More precise ly\, the original variant of RP serves to link Euclidean field theory (mat h) to relativistic quantum field theory (physics). Thereby linking diffic ult questions for relativistic quantum fields\, on one side\, with\, on th e other side\, Euclidean fields. Tools and solutions available on one side have often yielded insights on the other side. The RP-axioms link the two . The basic symmetry groups are different\, i.e.\, the Poincare group vs t he Euclidian group. Hence the associated harmonic analysis and spectral th eory are different of course. In recent work by the speaker and multiple c o-authors have aimed to expand the framework of RP to the theory of repres entations of Lie group\, spectral theory\, and operator algebras. Among ot her things\, this viewpoint yields insight into the role of the Markov pro perty\, as opposed to Osterwalder-Schrader positivity.\n\nAs a general pri nciple\, the Reflection positivity (RF) correspondence has proved useful i n mathematics and in many neighboring areas. In its original form\, RP suc cessfully combines powerful tools from analysis\, from geometry\, from rep resentation theory to questions in quantum physics. For example\, due to w ork by many authors\, the RF-correspondence has served to link abelian (co mmutative) properties of Gaussian processes/fields in the Euclidean settin g\, to the context of non-commutativity in the study of quantum fields. An d by now\, RP has further become a powerful tool in non-commutative harmon ic analysis\, and in the theory of unitary representations of Lie groups.\ n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Sahand Seifnashri (IAS Princeton) DTSTART:20221018T153000Z DTEND:20221018T170000Z DTSTAMP:20260422T225657Z UID:MathematicalPhysics/71 DESCRIPTION:Title: Non-Invertible Symmetries and their Representations\nby S ahand Seifnashri (IAS Princeton) as part of Wales MPPM Mathematical Physic s\n\n\nAbstract\nI will discuss generalized symmetries in two-dimensional QFTs that can be non-invertible. Such finite non-invertible symmetries are described by a fusion category rather than a finite group. Using the resu lts in the mathematical physics literature\, we find the appropriate notio n of representation for non-invertible symmetries needed to derive selecti on rules on correlation functions. We use this understanding to derive a C ardy-like formula for 2d CFTs with a finite non-invertible symmetry. More specifically\, we derive a universal formula for the asymptotic density of states transforming in an irreducible representation of a fusion category symmetry.\n\nBased on arXiv:2208.05495 and in collaboration with Ying-Hsu an Lin\, Masaki Okada\, and Yuji Tachikawa.\n LOCATION:https://researchseminars.org/talk/MathematicalPhysics/71/ END:VEVENT END:VCALENDAR