# Next Week @ the SCGP

Tuesday, 4-4-2017

SCGP Weekly Talk: Dmitry Orlov

Time: 1:00 PM - 2:00 PM

Location: SCGP 102

Description: Title: Quivers, noncommutative varieties, and their geometric realizations.
Abstract: Considering some special examples as algebras of quivers with relations I will give an informal introduction to a theory of geometric realizations of noncommutative and derived varieties. I also consider examples of noncommutative projective planes and the quiver of Ising model. Some relations to mirror symmetry will be discussed as well.
#weeklytalk

Wednesday, 4-5-2017

Special algebraic geometer Seminar: Dmitry Orlov

Time: 1:30 PM - 2:30 PM

Location: SCGP 313

Description: Title: Geometric realizations of noncommutative varieties and phantoms.
Abstract: In my talk I am going to discuss such phenomena as phantom and quasi-phantom categories which appear as admissible subcategories in derived categories of coherent sheaves on fake del Pezzo surfaces. They give examples of smooth and proper noncommutative varieties whose additive invariants are almost or completely trivial. I am also going to discuss general notions of noncommutative varieties and their geometric realizations.

Thursday - April 6, 2017

**YITP Event:**Martin Kruczenski (Purdue) [THEORY]

Time: 2:30 PM - 3:30 PM

Location: YITP seminar room

Description: Loop Equations and bootstrap methods in the lattice
Abstract: Gauge theories can in principle be formulated purely in terms of gauge invariant quantities, a fact which is made manifest, for example, by the AdS/CFT correspondence that reformulates a gauge theory as a closed string theory. More directly, one can describe a gauge theory in terms of the expectation value of Wilson loops. Such expectation values obey the so-called loop equation and therefore it is an important question if such equation is enough, at least in principle to determine the value of the Wilson loops.
In this talk I will consider the loop equation for Wilson loops defined in a pure Yang-Mills lattice gauge theory in the large-N limit. With the lattice as a regularization, the loop equation becomes a well-defined equation for a discrete set of quantities. However, we argue that, in general, the solution to the loop equation is not unique. In particular in the weak coupling phase relevant for the continuum limit, the loop equation needs to be suplemented by the condition that certain matrices whose entries are Wilson loops expectation values are positive definite. The best approach turns out to be to put bounds on the possible values of the Wilson loops by using the loop equation and the positivity condition to formulate a semi-definite programming problem that can be solved by using standard methods. We will present results for two, three and four dimensions and a preliminary discussion of the N=4 SYM case. Although presently the results are not as accurate as those that can be obtained by direct lattice numerical simulations they seem to indicate that a formulation in terms of Wilson loops is indeed possible if the extra conditions are included. Furthermore the positive definite matrices lead to other results, for example the definition of an entropy associated with the Wilson loops.

Friday, 4-7-2017

Closing Reception: Oakes Twins Sightlines Art Exhibition

Time: 5:00 PM - 7:00 PM

Location: SCGP Lobby and Art Gallery

Description: Visit http://scgp.stonybrook.edu/archives/20305 for more information

Thursday - April 13, 2017