Welcome!
From July 20 to 22, 2017, the Mathematical Physics group in the Mathematisches Institut at Universität
Heidelberg will host a threeday workshop on recent topics at the intersection of Physics and Geometry. The
workshop is intended to serve as an unofficial satellite workshop of
String Math 2017, held in Hamburg July 24–29.
Confirmed speakers

Matthew Bullimore (Oxford)

Alexey Bondal* (Moscow)

Mykola Dedushenko (Pasadena)

Ori Ganor (Berkeley)

Owen Gwilliam (Bonn)

Justin Hilburn (Philadelphia)

Kentaro Hori (Tokyo)

Si Li (Beijing)

Hyenho Lho (Zurich)

Mauricio Romo (Princeton)

Piotr Sułkowski (Warsaw)

Piljin Yi (Seoul)

Michele del Zotto (Stony Brook)

...

...
(*) tentative
Description
Many of the equations that govern the mathematical applications of
quantum field theory and string theory arise as flatness equations, either directly
from the nilpotency of supervariations, or indirectly during a gaugefixing procedure.
In fact, dressed up with moduli and upon quantization, flat connections have been claimed to
encompass our entire subject. An elementary but rich example are the moduli \( M_{\rm flat} \) of
flat connections over Riemann surfaces, which occur as phase space of ChernSimons
theory, and whose quantization leads to the computation of dimensions of spaces of sections
of certain bundles over \( M_{\rm flat}\). In the process, the theorem of NarasimhanSeshadri
identifies \( M_{\rm flat} \) with the moduli space of holomorphic
vector bundles, which in turns allows one to describe them much more explicitly and concretely. When
\( G_{\mathbb C} \) is a complex Lie group and \(G\) its compact real form,
\( M_{\rm flat}(G_{\mathbb C})\) can be identified with the moduli space of \(G\)Higgs bungles,
connecting \(M_{\rm flat}\) to Hitchin's integrable systems, another flatness landmark.
This workshop views \( M_{\rm flat} \) and related ideas as the backdrop to many recent
developments, a catalyst for progress, and a synecdoche for the many surprising
connections between gauge theory, string theory, geometry and topology.
Our idea is to bring together
researchers in whose work \( M_{\rm flat} \) makes unusual or surprising appearances: people
who have used or developed new or unusual techniques to study \( M_{\rm flat} \), who have
proposed analogues of \( M_{\rm flat}\), or who may not even think of themselves as
studying flat connections at all. We hope that
people with different viewpoints on
these connections will be able to benefit from one another's perspectives this Summer.
The workshop program will highlight recent applications of flat connections in
analyzing BPS spectra, Dbrane transport and stability, illustrate the power
of homological algebra and derived algebraic geometry to address real physical
problems, and showcase recent trends emerging from arithmetic questions,
including flux quantization in string theory and various analogies between Galois symmetries in
number theory and global and local symmetries in gauge theory.
We hope the conference will be fairly unique in bringing together mathematicians working on factorization
algebras in QFT and physicists working on categorification, knot homologies, and defects in supersymmetric QFTs.
Program
The three days are grouped thematically.
Thursday, July 20
Time 
Speaker 
Title, Abstract 
9:30am 
Ganor 
Quadratic Reciprocity and Janus Configurations 

abstract goes here...

Coffee break

11:00am 
Sułkowski 
Knots are quivers? 

I will present a surprising relation between knot invariants
and quiver representation theory, motivated by various string theory
constructions involving BPS states. Consequences of this relation
include the proof of the famous LabastidaMarinoOoguriVafa
conjecture, explicit (and unknown before) formulas for colored HOMFLY
polynomials for various knots, new viewpoint on knot homologies, new
dualities between quivers, and many others. The crucial role in this
relation is play by Apolynomials  which represent certain flat
connections in ChernSimons theory  and their quantization.

Lunch break 
1:30pm 
Bullimore 
TBA 

abstract goes here...

3:00pm 
Yi 
TBA 

abstract goes here...

4:15pm 
del Zotto 
TBA 

abstract goes here...

Friday, July 21
Time 
Speaker 
Title, Abstract 
9:30am 
Bondal 
TBA 

abstract goes here...

Coffee break

11:00am 
Gwilliam 
ChernSimons theory and Koszul duality 

The observables of perturbative ChernSimons theory naturally form an algebra over the
little 3disks operad, as I will explain. In consequence, line operators form a braided
monoidal category. We then use higher abstract nonsense, notably Koszul duality, to recover
a quantum group with formal parameter. This work in progress is joint with K. Costello and
J. Francis.

Lunch break 
1:30pm 
Lho 
TBA 

abstract goes here...

3:00pm 
Li 
TBA 

abstract goes here...

4:15pm 
Hilburn 
TBA 

abstract goes here...

Saturday, July 22
Time 
Speaker 
Title, Abstract 
9:30am 
Hori 
TBA 

abstract goes here...

Coffee break

11:00am 

TBA 

abstract goes here...

Lunch break 
1:30pm 
Dedushenko 
Fourmanifold invariants and 2d CFT 

Recently, it has been conjectured that there exists a class of 2d N=(0,2) SCFTs T[M_4, G],
labeled by a 4manifold M_4 and a Lie group G, which could provide a new type of smooth structure
invariants for M_4. Such theories are given by twisted compactifications of the 6d (2,0) theory on M_4.
We study one of the simplest cases when G=U(1). Even though such T[M_4, U(1)] looks trivial
(in particular, it is free), from the string theory point of view, it is natural to include
certain local defect operators in this theory. They are naturally defined in the UV, while in
the IR description they explicitly depend on the SeibergWitten (SW) invariants of
M_4. T[M_4, U(1)] perspective leads to the equivariant multimonopole generalization of
SW invariants. We study them from several points of view, including the 4d gauge theoretic
approach, and identify the structure of the VOA T[M_4, U(1)]. We also propose some further
directions for generalizations, including the case of nonabelian G.

3:00pm 
Romo 
TBA 

abstract goes here...

Practical Information
Venue
All talks will be held in the 5th floor Conference Room (5/104) in the Southern wing
of the
MATHEMATIKON.
Morning and afternoon coffee/tea and lunches will be served in the 5th floor common room.
Accommodation and Provisioning
The Heidelberger Hof
hotel is conveniently located midway
between the Neuenheimer Feld and the main attractions of old town Heidelberg.
For a fast bus connection to Campus, board route 31 at Bismarckplatz, headed
to Kopfklinik
(not Universitätsplatz!) and get off 5 stops later at Bunsengymnasium. The main
entrance of the
MATHEMATIKON is across the street.
Shops and restaurants are in the middle and Northern wing.
The pleasant walk from Bismarckplatz across the bridge, down the Neckar river, and up Berliner
Strasse takes about 25 minutes.
Registration and Workshop Dinner
There is no registration fee, however we ask that all those interested in attending
the talks send us an
Email ahead of time, so we may have an idea of the number of prospective participants.
(We reserve the right to raise a guard in the unlikely event of a general stampede.)
In your message, please indicate whether or not you are interested in joining us for the
workshop dinner on Friday night. You will be asked for a € 20 contribution for the dinner;
further information to follow.
Organizers
For any further information, please send us an
Email
Sponsors