## Beijing Geometry and Physics Colloquium (Satellite Conference of STRING 2016)

**Speaker(s): ** Several Speakers

**Time: **July 30 - July 31, 2016

**Venue: ** Lecture Hall, Jiayibing Building,Jingchunyuan 82, BICMR

**Beijing
Geometry and Physics Colloquium**

**(Satellite Conference of STRING 2016)
**

During last decade, the most active area between geometry and physics is in the area of 6d little string theory/6d conformal field theory. The lower dimensional compactification of unknown 6d little string theory yields such popular topics as AGT conjecture. 3d/3d mirror symmetry.

Taking the advantage of String 2016 in Beijing, we will invite some top experts of the field to have a two day event of Beijing Geometry and Physics colloquium at July 30-31 at Beijing International Center for Mathematics Science. All the lecture will be in the lecture hall of 甲乙丙楼。

Directions to BICMR

Here is a tentative schedule

__July
30__

2:00pm-3:00pm

Kazuya
Yonekura (IPMU)

Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge
theories

3:00pm-3:30pm

Tea Time

3:30pm-4:30pm

Xi Yin

TBA

4:45pm-5:45pm

Babak Haghighat (Tsinghua University)

6d SCFTs and Calabi-Yau manifolds

__July
31__

9:30am-10:30am

Kevin Costello (Periemeter Institute)

M-theory, non-commutative gauge theory, and holography for M5 branes

10:30am-11:00am

Tea
Time

11:00am-12:00

Thomas Dumitrescu (Harvard)

Anomalies, RG Flows, and the a-Theorem in Six Dimensions

2:00pm-3:00pm

Mina Aganagic (Berkeley)

Two mathematical applications of little string theory

3:00pm-3:30pm

Tea Time

3:30pm-4:30pm

Kimyeong Lee (KIAS)

TBA

4:45pm-5:45pm

Sergei Gukov (Caltech)

Fivebranes on 3-manifolds and 4-manifolds

Title and abstract:

*Kazuya Yonekura (IPMU)*

Title: Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories

Abstract: I will talk about a bottom-up approach based on instanton operators to see symmetry enhancement in 5d gauge theories.

In particular I will discuss when 5d gauge theories are expected to be lifted to 6d SCFTs, focusing on the case of SU(N) quiver gauge theories.

*Babak Haghighat (Tsinghua University)*

Title: “6d SCFTs and Calabi-Yau manifolds”

Abstract: We review recent developments in computing BPS partition functions of 6d SCFTs. These can be engineered through elliptically fibered non-compact Calabi-Yau manifolds and the partition functions are equivalent to topological string partition functions of the relevant Calabi-Yau. We show how these partition functions can be computed in terms of elliptic genera of solitonic strings which appear on the tensor branch of the 6d SCFT. The elliptic genus is a meromorphic Jacobi form in the fibre modulus and encodes all-genus information about enumerative invariants of the Calabi-Yau. Furthermore, we show how the partition function can be used to compute Donaldson-Thomas invariants associated to elliptic surfaces. Finally, we present a method for obtaining the mirror Calabi-Yau as an emergent geometry in the limit of large string charge.

*Kevin Costello (Periemeter Institute)*

Title: M-theory, non-commutative gauge theory, and holography for M5 branes

Abstract: I'll give a definition of supergravity in an Omega background, and argue that 11 dimensional supergravity when placed in a certain Omega background is equivalent to a 5 dimensional non-commutative gauge theory. M5 and M2 branes become natural gauge-theoretic objects, namely t'Hooft operators and instanton particles. Using an approach to holography developed with Si Li, we can use this picture to analyze the algebra of operators on M5 branes in the Omega background, in the large N limit. We find this algebra becomes a certain Yangian studied by Maulik-Okounkov. This analysis provides a holographic derivation of their result that this Yangian acts on the cohomology of instanton moduli spaces.

*Mina Aganagic (Berkeley)*

Title: “Two mathematical applications of little string theory”

Abstract: I will describe two mathematical applications of little string theory. The first leads to a variant of AGT correspondence that relates q-deformed W algebra conformal blocks to K-theoretic instanton counting. This correspondence can be proven for any simply laced Lie algebra. The second leads to a variant of quantum Langlands correspondence which relates q-deformed conformal blocks of an affine Lie algebra and a W algebra, associated to a Langlands dual pair of Lie algebras. The proof of the correspondence for simply laced Lie algebras involves, in a crucial way, the recently discovered elliptic stable envelopes.