I am very proud of my graduate students:

(below I list works done during their time at Kent State only)

        Wei Bai, Galyna Livshyts, A.Z. and Matt Alexander in Spring 2014.

                                        photo by Robert Christy.

 

Matthew Alexander.

Matt is my current Ph.d. student. We are working on (and learning about) new directions in Discrete Geometry and especially problems related to Geometric Tomography and Convex Geometry. Very recently we with Matt were able to prove a discrete analog of Koldobsky’s slicing inequality, which we are currently writing down and prepare for publication.

Jeffrey Schlaerth.

Jeff is my current Ph.d. student. The main subject of his  work is a Fourier analytic approach to geometric tomography. Jeff  is planing to graduate this year. 


J. Schlaerth, “Local and equatorial characterization of unit balls of subspaces of $L^p$, $p>0$ and properties of the generalized cosine

transform”,  J. Math. Anal. Appl.,  vol. 382, no. 2, (2011), 523--533.

 

Jaegil Kim.

Jaegil graduated with Ph.D. in 2013 and currently a Postdoctoral Fellow at the University of Alberta, Edmonton. Jaegil’s  thesis contains may interesting observation on the local version of Mahler's conjecture (including a complete solution for Hanner polytopes). Jaegil also done a number of very interesting works on the geometry of Intersection bodies.


J. Kim and S. Reisner,  “Local minimality of the volume-product at the simplex,” Mathematika, 57 (2011), no 1,  121--134.


J. Kim, V. Yaskin, and  A. Zvavitch, “The geometry of p-convex intersection bodies”Adv. Math., 226, (2011), no 6, 5320--5337.


J. Kim, “Minimal volume product near Hanner polytopes”J. Funct. Anal., 266 (2014), no. 4, 2360– 2402.


J. Kim and A. Zvavitch, “Stability of the reverse Blaschke-Santalo inequality for unconditional convex bodies” Proc. Amer. Math. Soc., 143 (2015), 1705-1717.


M. Alfonseca and J. Kim,  “The iteration of intersection body operators for bodies of revolution”,   Canad. J. Math., 67(2015), no. 1, 3-27.

 

Galyna Livshyts.


Galyas Ph.d. thesis was concentrated on different types of isoperimetric inequalities for log-concave measures. She defended her thesis in Spring of 2015 and now is an Assistant Professor at the Georgia Institute of Technology.


G. Livshyts, ”Maximal surface area of a convex set in $\R^n$  with respect to exponential rotation invariant measures,” J. Math. Anal. Appl.,  404,  2,  (2013),  231--238.


G. Livshyts, “Maximal surface area of a convex set in ${\mathbb R}^n$ with respect to log concave rotation invariant measures,”  GAFA Seminar Notes, 2116, (2014), 355-383.


G. Livshyts, “Maximal Surface area of Polytopes with Respect to log-concave rotation invariant measure,” (2014), to appear in Adv. Appl. Math.


G. Livshyts, “On the Gaussian concentration inequality and its relation to the Gaussian surfacer area,” in preparation.


G. Livshyts, A. Marsiglietti, P. Nayar, A. Zvavitch, “On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric type-inequalities”, submitted.

 

Wei Bai.


Wei finished her Master thesis in Percolation Theory and graduated in Spring 2014.

Yuanyuan Peng.


Yuanyuan have finished her Master thesis in Random Matrix Theory and graduated in Summer 2015.