Women In Mathematics in Atlanta, Georgia

All the mathematicians in the Atlanta area, at all stages in their career are welcome to participate! The talks are intended for a general audience.

Contact:
Yulia Babenko, Kennesaw State University,

ybabenko@kennesaw.edu

Galyna Livshyts, Georgia Institute of Technology,
glivshyts6@math.gatech.edu

Location: Georgia Institute of Technology, Skiles bldg room 006, 686 Cherry St NW, Atlanta, GA 30313.

Schedule for Spring 2018:

January 17: cancelled due to snow;

 

January 31: Olivia Beckwith, Emory University.

Title: Arithmetic in quadratic fields
Abstract: Quadratic fields arise naturally in the study of primes and in solving Diophantine equations. Their arithmetic is in many ways similar to the familiar arithmetic of whole numbers, but an important difference is that in quadratic fields, integers cannot be factored uniquely into primes. Class numbers measure the degree to which unique factorization fails, and it turns out that consequences of deep knowledge about these numbers percolate through virtually every important question in number theory. We’ll look at some of the rich history in the study of class numbers and at important questions that are the subject of current research.

 

February 14:  Rachel Kuske, Georgia Institute of Technology.

Title: New patterns in stochastic PDE’s with Pyragas control
Abstract: We provide a multiple time scales analysis for the Swift-Hohenberg equation with delayed feedback via Pyragas control, focusing on Turing bifurcations with and without additive noise. In the deterministic case, a Ginzburg-Landau-type modulation equation is derived that inherits Pyragas control terms from the original equation. The Eckhaus stability criteria is obtained for the rolls, with the delay driving the appearance of an intermediate time scale observed in the transients. In the stochastic context, slow modulation equations are derived for the amplitudes of the primary modes that are coupled to a fast Ornstein-Uhlenbeck-type equation with delay for the zero mode driven by the additive noise. By deriving an averaging approximation for the amplitude of the primary mode, we show how the interaction of noise and delay influences the existence and stability range for the noisy roll-type patterns. Furthermore, approximations for the spectral densities of the primary and zero modes show that oscillations on the intermediate times scale are sustained through the phenomenon of coherence resonance. These dynamics on the intermediate time scale are sustained through the interaction of noise and delay, in contrast to the deterministic context where dynamics on the intermediate times scale are transient.

 

February 28: Alexandra Smirnova, Georgia State University.

Title: Disease forecasting by new regularized Broyden-type optimization algorithms
Abstract: In this talk, we will outline a new approach to the development of iteratively regularized Broyden-type algorithms for solving nonlinear ill-posed inverse problems in either finite or infinite dimensional spaces. The novel regularization methods are designed to solve large-scale unstable least squares problems, where the Jacobian of a discretized nonlinear operator is difficult or even infeasible to compute. To face this challenge, a family of Gauss-Newton and Levenberg-Marquardt algorithms with the Fréchet derivative operator recalculated iteratively by using Broyden-type single rank updates is considered. To balance accuracy and stability, the pseudo-inverse for the derivative-free Jacobian is regularized in a problem-specific manner at every step of the iteration process. The study has been motivated by applications of inverse problems in epidemiology and infectious disease modeling, where stable estimation of key epidemiological parameters at the onset of an emerging virus is paramount in assisting public health authorities to rapidly assess the situation in order to determine whether the pathogen in question is capable of generating sustained local or global outbreaks. To illustrate theoretical findings, numerical simulations for both parameter estimation and forecasting of future incidence cases will be presented.

 

March 14Amalia Culiuc, Georgia Institute of Technology.

Title: Sparse domination principles for singular integral operators
Abstract: The estimation of singular integrals, which are generally non-local and non-positive operators, by sparse forms, which by contrast are positive and localized, has recently become a leading trend in Calderon-Zygmund theory and beyond. In this talk we will explore the concept of sparse domination and its implications for weighted norm inequalities. In particular, we will discuss several sparse domination results, including the study of the bilinear Hilbert transform and rough homogeneous singular integrals.

 

March 28: Kirsten Wickelgren, Georgia Institute of Technology.

   Title: How to count lines on a cubic surface

Abstract: I’ll introduce some enumerative geometry, algebraic topology, and A1 or motivic algebraic topology, and then discuss a joint result with Jesse Kass giving a generalization to all fields of characteristic not 2 of the classical enumerative result that there are 27 lines on a smooth cubic surface defined over the complex numbers

April 11:  Samantha Petti, Georgia Institute of Technology.

   Title: Graph Approximation: Szemer\’edi’s regularity lemma, graph limits, and the ROC model

Abstract: How can we approximate sparse graphs and sequences of sparse graphs (with average degree unbounded and o(n))? We consider convergence in the first k moments of the graph spectrum (equivalent to the numbers of closed k-walks) appropriately normalized. We introduce a simple, easy to sample, random graph model that captures the limiting spectra of many sequences of interest, including the sequence of hypercube graphs. The Random Overlapping Communities (ROC) model is specified by a distribution on pairs (s,q), s∈ℤ+,q∈(0,1]. A graph on n vertices with average degree d is generated by repeatedly picking pairs (s,q) from the distribution, adding an Erd\H{o}s-R\'{e}nyi random graph of edge density q on a subset of vertices chosen by including each vertex with probability s/n, and repeating this process so that the expected degree is d. Our proof of convergence to a ROC random graph is based on the Stieltjes moment condition. We also show that the model is an effective approximation for individual graphs. For almost all possible triangle-to-edge and four-cycle-to-edge ratios, there exists a pair (s,q) such that the ROC model with this single community type produces graphs with both desired ratios, a property that cannot be achieved by stochastic block models of bounded description size. Moreover, ROC graphs exhibit an inverse relationship between degree and clustering coefficient, a characteristic of many real-world networks.

 

Schedule for Fall 2018:

Event 1:

Friday, September 21, Skiles 006, 

686 Cherry St NW, Atlanta, GA 30311

 11:30 am: refreshments

 12 pm: Laura Eslava Fernandez, Georgia Institute of Technology.

    Title: Hubs in random trees: Fate or fluke?

Abstract: In social networks, we usually find nodes that are directly connected to a large portion of the network’s nodes. These    nodes are called hubs. How do such hubs arise? Where can we find them?

In this talk, we consider two probabilistic toy-models of random networks that generate random trees. These are the precedent for the preferential attachment models introduced by Albert and Barabasi in 1999. We discuss how the choice of randomness prompts stark differences in the behavior of hubs, even in seemingly simple models such as random trees.

  12:50 pm: refreshments, break

  1:10 pm: Megan Bernstein, Georgia Institute of Technology.

Title: Algebraic Voting Theory for Committee Voting and the Representation Theory of Wreath Products

   Abstract: Consider the problem of selecting an n-member committee made up of one of m candidates from each of n distinct departments. Using an algebraic approach, we analyze positional voting procedures in which you get to rank multiple candidates/committees, including the Borda count, as $\mathbb{Q}S_m \wr S_n$-module homomorphisms.
In particular, we decompose the spaces of voter preferences and election results into simple $\mathbb{Q}S_m \wr S_n$-submodules and apply Schur’s Lemma to determine the structure of the information lost in the voting process. We conclude with a voting paradox result, showing that for sufficiently different weighting vectors, applying the associated positional voting procedures to the same set of votes can yield arbitrarily different election outcomes.
Joint work with Hélène Barcelo, Sarah Bockting-Conrad, Erin McNicholas, Kathryn Nyman, and Shira Viel

 

 

Event 2:

Friday, October 26, Skiles 006, 

686 Cherry St NW, Atlanta, GA 30311

 

  11:30 am: refreshments

  12 pm: Christine Heitsch, Georgia Institute of Technology.

    Title: TBA

Abstract: TBA

 12:50 pm: refreshments, break

 1:10 pm: Victoria Powers, Emory University.

Title: TBA

   Abstract: TBA

 

 

Schedule for Spring 2019:

 

Event 1:

Friday, TBA, Skiles 006, 

686 Cherry St NW, Atlanta, GA 30311

                                                       

 11:30 am: refreshments

 12 pm: Mariana Montiel, Georgia State University.

    Title: TBA

Abstract: TBA

 12:50 pm: refreshments, break

 1:10 pm: Jennifer Hom, Georgia Institute of Technology.

Title: TBA

   Abstract: TBA

 

 

Event 2:

Friday, TBA, Skiles 006, 

686 Cherry St NW, Atlanta, GA 30311

                                                       

 11:30 am: refreshments

 12 pm: TBA

    Title: TBA

Abstract: TBA

 12:50 pm: refreshments, break

 1:10 pm: Shahaf Nitzan, Georgia Institute of Technology.

Title: TBA

   Abstract: TBA