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Series: Geometry Topology Seminar

Series: Combinatorics Seminar

Series: Joint ACO and ARC Seminar

Is matching in NC, i.e., is there a deterministic fast parallel
algorithm for it? This has been an outstanding open question in TCS for
over three decades, ever since the discovery of Random NC matching
algorithms. Within this question, the case of planar graphs has remained
an enigma: On the one hand, counting the number of perfect matchings is
far harder than finding one (the former is #P-complete and the latter
is in P), and on the other, for planar graphs, counting has long been
known to be in NC whereas finding one has resisted a solution!The
case of bipartite planar graphs was solved by Miller and Naor in 1989
via a flow-based algorithm. In 2000, Mahajan and Varadarajan gave an
elegant way of using counting matchings to finding one, hence giving a
different NC algorithm.However, non-bipartite
planar graphs still didn't yield: the stumbling block being odd tight
cuts. Interestingly enough, these are also a key to the solution: a
balanced odd tight cut leads to a straight-forward divide and conquer NC
algorithm. The remaining task is to find such a cut in NC. This
requires several algorithmic ideas, such as finding a point in the
interior of the minimum weight face of the perfect matching polytope and
uncrossing odd tight cuts.Joint work with Nima Anari.

Wednesday, November 15, 2017 - 13:55 ,
Location: Skiles 006 ,
Surena Hozoori ,
Georgia Tech ,
Organizer: Jennifer Hom

Series: Analysis Seminar

Series: Algebra Seminar

Given a Galois cover of curves X to Y with Galois group G which is totally ramified at a point x and unramified elsewhere,
restriction to the punctured formal neighborhood of x induces a Galois extension of Laurent series rings k((u))/k((t)). If
we fix a base curve Y , we can ask when a Galois extension of Laurent series rings comes from a global cover of Y in this
way. Harbater proved that over a separably closed field, this local-to-global principle holds for any base curve if G is a
p-group, and gave a condition for the uniqueness of such an extension. Using a generalization of Artin-Schreier theory to
non-abelian p-groups, we characterize the curves Y for which this lifting property holds and when it is unique, but over
a more general ground field.

Series: Geometry Topology Seminar

Monday, November 13, 2017 - 13:55 ,
Location: Skiles 005 ,
Tuo Zhao ,
Georgia Tech ,
Organizer: Wenjing Liao

Series: GT-MAP Seminars

TBA

Series: Stochastics Seminar