We are writing to announce the workshop, Yangians and Quantum Loop 
Algebras, to be held May 5-9th, in the vicinity of Austin, TX.  The workshop will 
be led by Valerio Toledano Laredo and Sachin Gautam.  I would be grateful if 
you could forward this email to Ph.D. students and recent Ph.D's who might be 
interested in applying.  We are accepting applications until Friday, February 7th.


The website for the workshop is: 
http://www.ma.utexas.edu/users/djordan/workshop.html


Thanks!
David Ben-Zvi and David Jordan

What and when

The week of May 5th-9th, we will be hosting a five-day workshop near Austin, 
TX for young researchers focusing on emerging algebraic aspects of quantum 
loop algebras, their representation theory, and their applications to solvable 
lattice models.

The workshop will be led by Valerio Toledano Laredo and Sachin Gautam.

Scientific program

Yangians and quantum loop algebras are two classes of infinite–dimensional 
quantum groups associated to a complex semisimple Lie algebra. They were 
first discovered in the mid–80s as symmetries of solvable models in Quantum 
Statistical Mechanics, specifically the Heisenberg XXX and XXZ spin chains. 
They have since appeared in a number of different contexts: Nakajima quiver 
varities, enumerative geometry, 4 and 5–dimensional supersymmetric gauge 
theories, scattering amplitudes to name a few.

The focus of this workshop will be on the algebraic aspects of these quantum 
groups, and their applications to solvable lattice models. The goal will be to 
familiarize the participants with the basics of these models (Yang–Baxter 
equations, Baxter’s transfer matrix formalism, Bethe Ansatz) and to explain 
how the Yangian and quantum loop algebra appear naturally. We will then cover 
their representation theory in some detail, and explain that their finite–
dimensional representations form a meromorphic braided tensor category. 
Finally, we will review some of the recent developments in this area, in 
particular the construction of a transcendental tensor equivalence between the 
two representation categories using abelian difference equations.

Participants should plan to each give a one-hour talk at the workshop. Topics 
for talks will be assigned by Valerio and Sachin, together with the organizers, 
based on particpant's background and interests.
The list of topics to be covered includes:  Vertex models, Bethe Ansatz, 
Yangians and quantum loop algebras, affine Lie algebras, Kac-Moody and loop 
presentations for quantum affine algebras, RTT and loop presentations for 
Yangians, their finite dimensional representations, meromorphic braided tensor 
categories, R-matrices for quantum affine algebra and Yangian, quantum KZ 
equations, trigonometric connections, Drinfeld's degeneration, difference 
equations, KZ functors.
A more complete list, with references, can be found on the website.
Accomodation and travel

Lodging and food will be provided near Austin in shared accommodation. 
Depending on funding, it may be possible to provide partial travel 
reimbursements, but participants should seek this primarily from their advisors 
or departments.

Who should apply, how to apply

Our ideal mix of participants will include both Ph.D students and recent Ph.D's. 
A background in quantum groups, affine Lie algebras, or representation theory 
more broadly is helpful but not required. Interested applicants should start by 
filling out the form linked on the website. We are accepting applications until 
February 7th.

Contact us

Please feel free to contact organizing commitee members David Jordan, David 
Ben-Zvi, Iordan Ganev, or Lee Cohn (emails available on the website) with any 
questions!

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