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.

I have co-advised Matt jointly with Matthieu Fradelizi. Matt have successfully defended his dissertation in Fall 2017. He was working on new directions in Discrete Geometry and especially problems related to Geometric Tomography and Convex Geometry. Matt. jointly with me and Marthin Henk) were able to prove a discrete analog of Koldobsky’s slicing inequality. Matt (jointly with me and Matthieu Fradelizi) done a lot of very interesting work on volume product.


M. Alexander, M. Henk and A. Zvavitch, “A discrete version of Koldobsky's slicing inequality” Israel Journal of Mathematics, to appear.


M. Alexander, M. Fradelizi and A. Zvavitch "Polytopes of Maximal Volume Product,” submitted.

Jeffrey Schlaerth.

Jeff worked with me from 2005 till 2014. The main subject of his work was Fourier analytic approach to geometric tomography.


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. After, till 2017 Jaegil worked as a PIMS Postdoctoral Fellow at the University of Alberta, Edmonton. Now Jaegil is working at Gwangju Institute of Science and Technology (GIST) in South Korea, 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 ${\mathbb R}^n$ 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,” Adv. Appl. Math., vol. 70, 54-69, (2015).


G. Livshyts, A. Marsiglietti, P. Nayar, A. Zvavitch, “On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric type-inequalities”, Transactions of the AMS, 369 (2017), no. 12, 8725–8742. .

 

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.

Norah Almuraysil.


Norah have finished her Master thesis in Spring 2017 and now is a lecturer at Imam Abdulrahman Bin Faisal University. During her time at Kent state Norah have worked on different measurements of non-convexity of a given sets, in particular studying how such measurements depend on the metric of a given space.