Group meetings

Spring 2024

Meeting Tuesdays 12-2pm in JCMB 5323

David is leading a new topic on higher form symmetries in holography and geometric engineering

18 Feb: Introduction to Differential Cohomology by Gianni

25 Feb: Differential cohomology in geometric engineering by Subri

4 March: Anomalies by Tudor

We start with our new topic on Koszul duality!

9 Jan: Introduction by Tudor

16 Jan: Intermezzo by Aiden about Associated Varieties

23 Jan: Math intro Koszul duality by Sarunas

30 Jan + 5 Feb: Intro to the physics behind Koszul duality by Tudor 

12 Feb: Introduction to Celestial Holography by Iustin

Fall 2023

Meeting Tuesdays 12-2pm in JCMB 5323

14 December: GRIFTerklaas 2023

Functorial CFT and conformal blocks (Nitu)

5 and 12 December: notes

Gerbes and Higher Gauge Theory (Dominik)

28 November and 5 December: notes

see also notes by Christian Saemann; and a paper with a simplicial formulation of higher gauge theory

 Factorization algebras

Nov 7 + 21: Clark (with notes from Jan) on the Langlands program and factorization algebras

Nov 14: Jan on factorization algebras  

26 September: We start with our mini-topic on AGT duality. The rough plan is:

Sept 26: Instanton counting in 4d N=2 theories Part I: equivariant integration and coh tft's - Loïc + Lotte

Oct 3: Virasoro VOA and conformal blocks - Gianni + Misha

Oct 10: Instanton counting in 4d N=2 theories Part 2: equivariant int + ADHM moduli space -> instanton counting

Oct 17: AGT in math: actions of Heis/W-alg on H^*(M_inst) - Lucien

Oct 24: AGT in phys: the 6d story - Subri 

19 September:  All-day workshop on Poisson and symplectic geometry, leading up to the LMS Hardy Lecture delivered by Eva Miranda. 

12 September: normal time 12-2pm

Lecture by Andy Neitzke on q-abelianization of local systems.

5 September: exceptional time 1-3pm

Welcome back! Research teasers by our guests Thomas Creutzig, Andy Neitzke and Joerg Teschner.

Spring 2023

Meeting Mondays 12-2pm in JCMB 5323

24 April

Lecture by Tudor on the topological twists of 3d N=4 gauge theories, and how to exploit them to access Higgs and Coulomb branches and higher structure.

17 April

Lecture 2 by Pavel on twists and supersymmetry algebras, focusing on topological twists in various dimensions.

10 April

Lecture 1 by Pavel on twists and supersymmetry algebras.

3 April

Lecture by Tudor on the menagerie of Higgs and Coulomb branches of 3d N=4 theories, brane constructions, and 3d mirror symmetry.

27 March

Lecture by Tudor: introduction to abelian duality in three dimensions. Though this is well known, and fundamental for all statements about 3d Coulomb branches, simple references are surprisingly difficult to pin down. Some references include:

• 3d abelian dualities with matter (e.g. particle-vortex duality) and Chern-Simons levels (e.g. 3d bosonization) in C. Turner's notes. All from a physics perspective.

• The closest to the approach Tudor took in the lecture: Hori-Vafa's discussion of T-duality  (section 2.2.1), which relates two dual S^1-valued scalars in 2d.

• A paragraph on p5 of Aharony-Hanany-Intriligator-Seiberg-Strassler (generalizing abelian duality to 3d N=2 SUSY)

• For a perturbative construction of quantum abelian dualities, in the BV formalism (though not focusing on 3d) see C. Elliott's paper.

Discussion by Subri on Chern-Simons theories for atmospheric waves

13 March

arXiv catchup

Assorted suggestions:

• One-loop corrections to the celestial chiral algebra from Koszul duality (Wei)

• On reconstructing finite gauge group from fusion rules (Linden)

• Bootstrapping non-invertible symmetries (Linden)

• Toric 2-group anomalies via cobordism (Linden)

• Chiral life on a slab (Tudor)

• Generalized symmetries and anomalies of 3d N=4 SCFT's; also this (Tudor)

• On the A-infinity category of a holomorphic moment map (Tudor)

January-February:

Lectures on cluster algebras and character varieties organised by Sasha!

• notes from Sasha's intro on cluster algebras

• notes from David on the Springer resolution

• notes from Subri about spectral networks

• notes from Matthew about quantization and quantum groups

• notes from Sasha about positive representation and Toda

Autumn 2022

Meeting Mondays 1-3pm in JCMB 1501

12 December

Presentation topic: Physics of 2d and 3d semisimple TQFT's, with examples from DW theory (Tudor)

Assorted papers to look at:

• Non-invertible Gauss law and axions

• Quiver diagonalization and open BPS states

• Bi-Yang-Baxter models and SL(2) orbits

• 1/3 BPS loops in ABJM theory

• Double quiver gauge theory and BPS/CFT correspondence

• Current algebra levels in the E8 theory

• Matrix factorizations and gl(m|k) quantum invariants

5 December

Presentation topic: DW theory as an extended TFT (continued - Iordanis)

Assorted papers to look at:

• Non-stationary difference equation, affine Laumon space and quantization of discrete Painleve equation

• Hecke relations among 2d fermionic RCFT's

• Classical freeness of orthosymplectic affine vertex superalgebras

28 November

Presentation topic: DW theory as an extended TFT (Iordanis)

Assorted papers to look at:

• Global symmetry-breaking and generalized theta-terms in Type IIB EFTs

• Phases of Wilson lines in CFT's

• Strong coupling expansions in N=2 quiver gauge theories

• Partition functions on squashed 7-spheres and holography

• Remarks on Berry connection in QFT, anomalies, and applications

• Higher-group symmetry in finite gauge theory and stabilizer codes

• Line defects in fermionic CFT's

• Enumerative geometry of surfaces and topological strings

• Cluster transformations, the tetrahedron equation, and 3d gauge theories

21 November

Presentation topic: examples of DW theory (Linden)

Assorted papers to look at:

• Neutrino masses from generalized symmetry breaking

• MSW compactifications of 6d N=1 SCFT's on 4-manifolds 

• Ginzburg-Laudau description and emergent supersymmetry of the (3.8) minimal model

• More on Seiberg-Witten theory and monstrous moonshine

• Argyres-Douglas avatars of Coulomb branch physics

• S^1 reduction of 4d N=3 SCFT's and squashing independence of ABJM theories

• Instances of higher geometry in field theory

• Gauging noninvertible defects: a 2-categorical perspective

• Anomalies and gauging of U(1) noninvertible symmetries in 4d QED

• A simple formula for the x-y symplectic transformation in topological recursion

• RG flows in 2d QCD

• Weyl group symmetry of q-characters

• A Goldstone theorem for continuous non-invertible symmetries

• Review of continuous anomalies and the Green-Schwarz mechanism

• d=5 holomorphic Chern-Simons and the pure spinor superstring

• 3 definitions of BF theory on homology 3-spheres

14 November

Presentation topic: DW theory continued (Benjamin)

Assorted papers to look at:

• Snowmass white paper on Physical Mathematics -- a massive review of some parts of the field

• Non-invertible symmetries of Class S theories

• A-infinity structures on non-orientable Lagrangians [1,2]

• Twisted VOA modules and their automorphisms

• Monopole operators and affine Grassmannian slices

• Extended operators and VOA's in 4d N=2 theories

• a construction of solutions to the Strominger system (heterotic string backgrounds, involving vector bundles over deformed CY's)

7 November

Presentation topic: Dijkgraaf-Witten theory (Benjamin)

Assorted papers to look at:

• Twisted holography without conformal symmetry

• Exact multi-instantons in topological string theory

• On the intermediate Jacobian on M5-branes

• Line operators in 4d CS theory and Cherkis bows

• Modular factorization of superconformal indices

• Classification of rank 1 5d N=1 and 6d (1,0) SCFT's

• An algebro-geometric approach to twisted indices of supersymmetric gauge theories (PhD thesis)

• Quantum differential equation for slices of the affine Grassmannian

• Holomorphic Foer theory and DT invariants

31 October

Presentation topic: Hilbert spaces in Chern-Simons continued (Juan Carlos)

Recap of the MSRI workshop "New four-dimensional gauge theories"

Assorted papers:

• Large N Superconformal Indices for 3d Holographic SCFTs

• Solitonic symmetry beyond homotopy: invertibility from bordism and non-invertibility from TQFT

• New Instantons for Matrix Models

• Emergent higher-form symmetry in Higgs phases with superfluidity

24 October

Presentation topic: Expectation values of Wilson loops in abelian Chern-Simons (Patrick)

Assorted papers:

• A holographic approach to the 6d superconformal index

• A pair of papers [1,2] relating 2d BF theory to Bose-Einstein condensates...   might be fun to decipher

• Liouville theory and the Weil-Petersson geometry of moduli space

• Electric-magnetic duality in a class of G2 compactifications of M-theory

• Exploring Seiberg-like N-alities

• Symmetries of CY prepotentials with isomorphic flops

• Wall crossing for K-theoretic quasimap invariants

17 October

Presentation topic: Hilbert spaces in Chern-Simons (Juan Carlos)

Assorted papers to look at:

• TQFT's and quantum computing

• Symmetry TFT's for 3d QFT's from M theory

• Three dimensional topological quantum field theory from U_q(gl(1|1)) and U(1|1) Chern-Simons theory

• Classifying BPS Wilson loops in 3d N=4 Chern-Simons-matter theories

• Exploring Seiberg-like dualities with eight supercharges

• Insertion of vertex operators using BV formalism

• Bethe state counting and the Witten index

• Modular linear differential equations for Hecke and Fricke groups