Extension theorems in vector spaces over finite fields Dr. Alex Iosevich. Journal reviewer for International Mathematics Research Notices.

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1 Doowon Koh T (517) B koh@math.msu.edu Education Aug.2003 Dec.2008 Dissertation Dissertation Supervisor Mar.1998 Feb.2000 Thesis Advisor Mar.1991 Feb.1998 Feb.1993 Apr.1995 Ph.D in Mathematics, University of Missouri, USA. Extension theorems in vector spaces over finite fields Dr. Alex Iosevich Master of Science in Mathematics, Chung-Ang University, Seoul, Korea. Oscillatory Integrals Dr. Yong-Kum Cho Bachelor of Science in Mathematics, Chung-Ang University, Seoul, Korea. Military Service. Professional Experience May,2011 Present Aug.2009 Present Dec.2008 May.2009 Aug.2003 Dec.2008 Mar.2003 Aug.2003 Sep.2001 Feb.2003 Mar.1998 Feb.2000 Journal reviewer for International Mathematics Research Notices. Postdoctoral Fellow,, USA. Mentor: Dr. Ignacio Uriarte-Tuero Visiting assistant professor, University of Missouri, USA. Teaching and Research Assistant, University of Missouri, USA. Part-time Lecturer, Chung-Ang University, Seoul, Korea. Teaching Assistant, Chung-Ang University, Seoul, Korea. Research Assistant, Chung-Ang University, Seoul, Korea. Research Interests Harmonic Analysis in Finite Fields, Fourier analysis, Geometric Combinatorics, Analytic Number Theory 1/5

2 Publications 1. D.Koh and C. Shen, Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields, Revista Matemática Iberoamericana, to appear in Volume 28, issue 1 (2012). 2. J.Chapman, M.B.Erdogan, D.Hart, A.Iosevich, and D. Koh, Pinned distance sets, k-simplices, Wolff s exponent in finite fields and sum-product estimates, Math. Z., currently published online, March 22 (2011). 3. D.Hart, A.Iosevich, D.Koh, and M.Rudnev, Averages over hyperplanes, sumproduct theory in vector spaces over finite fields and the Erdös-Falconer distance conjecture, TAMS, Volume 363, Number 6, June (2011), Pages A.Iosevich and D.Koh, Extension theorems for paraboloids in the finite field setting, Math. Z. 266 (2010), no.2, A.Iosevich and D.Koh, Extension theorems for spheres in the finite field setting, Forum Math. 22 (2010), no.3, D.Covert, D.Hart, A.Iosevich, D.Koh, and M.Rudnev, Generalized incidence theorems, homogeneous forms and sum-product estimates in finite fields, European J. Combin. 31 (2010), no. 1, A.Iosevich and D.Koh, Extension theorems for the Fourier transform associated with nondegenerate quadratic surfaces in vector spaces over finite fields, Illinois J. Math. 52 (2008), no. 2, A.Iosevich and D.Koh, The Erdös-Falconer distance problem, exponential sums, and Fourier analytic approach to incidence theorems in vector spaces over finite fields, SIAM J. Discrete Math. 23 (2008/09), no. 1, Submitted papers for publication 1. Extension and averaging operators in vector spaces over finite fields, joint work with Chun-Yen Shen, Submitted for publication, (2011). 2. The generalized Erdös-Falconer distance problems in vector spaces over finite fields, joint work with Chun-Yen Shen, Submitted for publication, (2011). 3. Additive energy and the Falconer distance problem in finite fields, joint work with Chun-Yen Shen, Submitted for publication, (2010). 4 Distance graphs in vector spaces over finite fields, coloring, pseudorandomness and arithmetic progressions, joint work with D.Hart, A. Iosevich, S.Senger,and I.Uriarte-Tuero, (2010). papers to be submitted soon 1. Mapping Properties of k-plane Transforms and Conical Surface Transforms in Finite Fields, (2011). 2/5

3 papers in preparation 1. L p L q estimates for Euclidean averaging operators, (2011). 2. Note on sharp X-ray and 2-plane transforms in finite fields, joint work with Chun-Yen Shen, (2011). 3. Fourier method and non-degenerate polynomials, joint work with Chun-Yen Shen, (2011). Unpublished preprints 1. Harmonic analysis related to homogeneous varieties in three dimensional vector spaces over finite fields, joint work with Chun-Yen Shen, (2010). 2. Extension and averaging operators for finite fields, (2009). 3. Note on the Minkowski dimension of distance sets inr 2, (2009), joint work with A.Iosevich, I.Uriarte-Tuero, and Y. Wang. April,2011 June,2010 Jan June,2009 Oct.2008 Mar.2008 Invited Talks Mapping properties of averaging operators in finite fields, Analysis, PDE and Mathematical Physics Seminar,MSU,East Lansing,MI. Harmonic analysis related to homogeneous varieties in three dimensional vector spaces over finite fields, Fields Institute-Harmonic Analysis:A Retrospective Workshop,Toronto,Ontario. Harmonic analysis in the finite field setting, Analysis, PDE and Mathematical Physics Seminar,MSU,East Lansing,MI. Extension theorems in the finite field setting, Analysis Seminar, Yonsei University, Seoul,Korea. Extension theorems for paraboloids and spheres in vector spaces over finite fields, Analysis and PDE Seminar, UCLA, Los Angeles, CA. Extension theorems for paraboloids in the finite field setting, AMS Special Session in Baton Rouge, Lousiana State Universtiy, Baton, LA. Feb Extension theorems for paraboloids in the finite field setting, Fields Institute - Workshop on Harmonic Analysis, Toronto, Ontario. Oct Oct Extension theorems for the Fourier transform associated with non-degenerate quadratic surfaces in vector spaces over finite fields, NSF FRG Conference-New Developments in Harmonic Analysis, University of Georgia, Athens, GA. The Erdös-Falconer distance problems, exponential sums, and Fourier analytic approach to incidence theorems in vector spaces over finite fields, FRG Seminar, University of Missouri, Columbia. 3/5

4 May 31-June 4, 2010 Aug.2008 Conferences Attended Harmonic Analysis: A Retrospective Workshop, Fields Institute, Toronto, Ontario. Summer school on Fourier analytic and probabilistic methods in geometric functional analysis and convexity, Kent State University,Kent,OH. Jun.2008 NSF-CBMS Ergodic Ramsey Theory Conference, Eastern Illinois University,Charleston,IL. Mar.2008 Feb.2008 Oct.2007 AMS Special Session in Baton Rouge, Lousiana State University, Baton, LA. Workshop on Harmonic Analysis, Fields Institute, Toronto, Ontario. New Developments in Harmonic Analysis, University of Georgia, Athens, GA. Teaching Experience Spring,2011 Fall,2010 Fall,2009 Fall,2008,2007, Winter,2007 Winter,2008, Fall,2006 Spring, 2003 Sep.2001 Feb.2003 Instructor, Calculus I,, USA. Instructor, Calculus I,, USA. Instructor, Analysis II,, USA. Teaching Assistant, Calculus I, University of Missouri, USA. Teaching Assistant, Calculus II in Honor s section, University of Missouri, USA. Part-time Lecturer, Calculus I, Linear Algebra, Chung-Ang University, Seoul,Korea. Teaching Assistant, Calculus I, Ordinary Differential Equation, Chung-Ang University, Seoul,Korea. Grants Support as a Research Assistant Summer, , Winter,2006 Summer 2004 Fall,2003 Winter,2004 Research Assistantship, supported by A. Iosevich under the United States National Science Foundation Collaborative Research Grant Analysis, Grant Number DMS Research Assistantship, supported by A. Iosevich under the United States National Science Foundation Grant in Classical Analysis, Grant Number DMS Graduate Fellowship, University of Missouri, USA. 4/5

5 References Alex Iosevich UR Mathematics University of Rochester Rochester, NY Ignacio Uriarte-Tuero Steve Hofmann University of Missouri Columbia, MO Terence Tao UCLA Los Angeles CA Jeanne Wald (Teaching) Alexander Volberg 5/5