The Graduate Student Seminar is a venue that any graduate student can use to present their work, to practice for an upcoming "official" talk, or just to discuss mathematical concepts they find interesting. We also invite Faculty to introduce their research to Graduate Students.

If you are interesting in giving a talk, please contact the chapter vice president, Andrew Pham (aapham@go.olemiss.edu)

Seminars in Fall 2017

10/13/2017

**Speaker**: Sashwat Tanay

**Title**: *Bivariate Power Series via a Perturbative Approach*

**Abstract**: Power series are one of the most important inventions in mathematics and have been employed to solve a myriad of problems in the physical science. There are multiple ways to obtain a power series (Taylor's formula, perturbative approach etc.) but the uniqueness theorem guarantees that all such methods yield the same answer. In this talk, the perturbative approach to obtain the power series (in two variables) is discussed. The perturbative approach is one where we first take into account only the leading order input information to obtain the leading order solution and gradually process the higher order terms of the input information to churn out the higher order terms of the solution as a power series. This happens order by order. This method is first demonstrated for the case of a much simpler univariate sine series because it captures the essence of the problem, which is then employed to the more complicated bivariate case. Finally, the physical context of this mathematical procedure is discussed briefly. The method finds application in simulating gravitational waves, which is crucial to their detection. The 2017 Nobel prize in physics was awarded to three key members of the LIGO collaboration (Profs. Weiss, Thorne and Barish) for their contributions to gravitational wave detections.

10/06/2017

**Speaker**: Khazhakanush Navoyan

**Title**: *Connected Spaces*

**Abstract**: Let X be a topological space. A separation of X is a pair of U, V of disjoint nonempty open subsets of X whose union is X. The space X is said to be connected if there does not exist a separation of X. Connectedness is obviously a topological property, since it is formulated entirely in terms of the collection of open sets of X. Said differently, if X is connected, so is any space homeomorphic to X. The definition of connectedness for a topological space is a quite natural one. One says that a space can be "separated" if it can be broken up into two "globs"- disjoint open sets. Otherwise, one says that it is connected.

09/08/2017

**Speaker**: Khazhakanush Navoyan

**Title**: *On Spectrum and Resolvent Set, Part 1*

**Abstract**: In this talk we deﬁne resolvent set and spectrum of a linear norm bounded operator T in a complex Banach space V. In particular, we deal with the case that V is a Banach lattice and the operator T is positive. We show that the spectrum is a closed and bounded set in the complex plane C and discuss the properties of spectral radius, which is the radius of the smallest circle having as its centre the origin and containing the spectrum..

Seminars before Fall 2017

March 3, 2017. Brent Holmes. University of Kansas. *Diameter of Graphs with a Strong Connectivity Property*.

February 10, 2017. Sooyeon Lee. *Beta Invariant of 3-connected Matroids*.

December 8, 2016. Jim Henegan. * The Reproducing Kernel of a Weighted Bergman Space*.

November 11, 2016. Dr. Sam Lisi. * A Brief Introduction to Morse Theory*.

October 14, 2016. Sasha Kocic. * Renormalization and Rigidity in Dynamical Systems*.

October 7, 2016. Zhenchao Ge. * The Size and Sign of a Gauss Sum*.

September 23, 2016. Stephan Roberts. * Polynomials over Infinite Dimensional Vector Spaces*.

September 9, 2016. Dr. Sandra Spiroff. * Min-plus Algebra*.

May 6, 2016. Katherine Perry. Auburn University. * Rainbow Spanning Trees in Edge-Colored Complete Graphs*.

March 31, 2016. Shaohui Wang. * Recent Results on the Ration of Domination and Independent Domination Numbers*.

February 12, 2016. Ali Dogan. University of Memphis. * On Saturation Games*.

November 12, 2015. Jiuhua Hu. Total Domination Polynomials of Graphs.

September 17, 2015. Brian Frazier.Towards a Proof of the Reconstruction Conjecture.

September 3, 2015. Roman Sverdlov. A Realistic Interpretation of Berezin Integrals.

May 1, 2015. Shaohui Wang, Multiplicative Zagreb Indices of Cactus Graphs.

April 17, 2015. Khazhak Navoyan. Riesz Representation Theorem.

January 30, 2015. Khazhak Navoyan. Examples of Banach Spaces.

November 20, 2015. Thomas Naugle. Noncommutative Geometry.

November 13, 2014. Shaohui Wang. Padmakar-Ivan Index of k-trees.

October 17, 2014. Sam Watson. Massachusetts Institute of Technology. *Random Fractal Curves in the Plane*.

May 2, 2014. Yongli Sang. Properties of Nonlinear Transformations of Non-Gaussian Linear Processes.

May 1, 2014. Janet Nakarmi. On Variable Bandwidth Kernel Estimation.

April 16, 2014. John Burt. (Visible) Tilings of Squares and Hypercubes.

March 6, 2014. Shaohui Wang. Multiplicative Zagreb Indices of k-trees.

April 11, 2014. Rebecca Winarski. Georgia Tech. *Braid Groups and Mapping Class Groups*.

February 27, 2014. Jim Henegan. Domain Coloring and the Visualization of Complex Valued Functions.