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Friday, February 23, 2018 - 13:55 ,
Location: Skiles 269 ,
Prof. Justin Kakeu ,
Morehouse University ,
Organizer: Sung Ha Kang

We use a stochastic dynamic programming approach to address the following question: Can a homogenous resource extraction model (one without extraction costs, without new discoveries, and without technical progress) generate non-increasing resource prices? The traditional answer to that question contends that prices should exhibit an increasing trend as the exhaustible resource is being depleted over time (The Hotelling rule). In contrast, we will show that injecting concerns for temporal resolution of uncertainty in a resource extraction problem can generate a non-increasing trend in the resource price. Indeed, the expected rate of change of the price can become negative if the premium for temporal resolution of uncertainty is negative and outweighs both the positive discount rate and the short-run risk premium. Numerical examples are provided for illustration.

Friday, February 23, 2018 - 10:00 ,
Location: Skiles 006 ,
Tim Duff ,
Georgia Tech ,
tduff3@gatech.edu ,
Organizer: Kisun Lee

TBA

Friday, February 23, 2018 - 10:00 ,
Location: Skiles 006 ,
Tim Duff ,
Georgia Tech ,
tduff3@gatech.edu ,
Organizer: Kisun Lee

Polyhedral homotopy methods solve a sparse, square polynomial system by deforming it into a collection of square "binomial start systems." Computing a complete set of start systems is generally a difficult combinatorial problem, despite the successes of several software packages. On the other hand, computing a single start system is a special case of the matroid intersection problem, which may be solved by a simple combinatorial algorithm. I will give an introduction to polyhedral homotopy and the matroid intersection algorithm, with a view towards possible heuristics that may be useful for polynomial system solving in practice.

Wednesday, February 21, 2018 - 14:00 ,
Location: Skiles 006 ,
Kevin Kodrek ,
GaTech ,
Organizer: Anubhav Mukherjee

There are a number of ways to define the braid group. The traditional definition involves equivalence classes of braids, but it can also be defined in terms of mapping class groups, in terms of configuration spaces, or purely algebraically with an explicit presentation. My goal is to give an informal overview of this group and some of its subgroups, comparing and contrasting the various incarnations along the way.

Series: Analysis Seminar

I will speak how to ``dualize'' certain martingale estimates related to the dyadic square function to obtain estimates on the Hamming and vice versa. As an application of this duality approach, I will illustrate how to dualize an estimate of Davis to improve a result of Naor--Schechtman on the real line. If time allows we will consider one more example where an improvement of Beckner's estimate will be given.

Series: Geometry Topology Seminar

Although the Alexander polynomial does not satisfy an unoriented skein relation, Manolescu (2007) showed that there exists an unoriented skein exact triangle for knot Floer homology. In this talk, we will describe some developments in this direction since then, including a combinatorial proof using grid homology and extensions to the Petkova-Vertesi tangle Floer homology (joint work with Ina Petkova) and Zarev's bordered sutured Floer homology (joint work with Shea Vela-Vick).

Series: CDSNS Colloquium

Using techniques from local bifurcation theory, we prove the existence of various types of temporally periodic solutions for damped wave equations, in higher dimensions. The emphasis is on understanding the role of external bifurcation parameters and symmetry, in generating the periodic motion. The work presented is joint with Brian Pigott

Series: Combinatorics Seminar

A tight k-uniform \ell-cycle, denoted by TC_\ell^k, is a k-uniform hypergraph whose vertex set is v_0, ..., v_{\ell-1}, and the edges are all the k-tuples {v_i, v_{i+1}, \cdots, v_{i+k-1}}, with subscripts modulo \ell. Motivated by a classic result in graph theory that every n-vertex cycle-free graph has at most n-1 edges, Sos and, independently, Verstraete asked whether for every integer k, a k-uniform n-vertex hypergraph without any tight k-uniform cycles has at most \binom{n-1}{k-1} edges. In this talk I will present a construction giving negative answer to this question, and discuss some related problems. Joint work with Jie Ma.

Friday, February 16, 2018 - 15:00 ,
Location: Skiles 271 ,
Yian Yao ,
GT Math ,
Organizer: Jiaqi Yang

I
will report on the parameterization method for computing normally
hyperbolic invariant tori(NHIT) for diffeomorphisms. To this end, a
Newton-like method for solving the invariance equation based on the
graph transform method will be presented with details.
Some notes on numerical implementations will also be included if time
allows.
This is a work by Marta
Canadell and Alex Haro.