Claremont McKenna College

850 Columbia Avenue

Claremont, CA 91711

Fax: (909) 621 - 8419

Webpage: http://math.cmc.edu/lenny/

__Citizenship:__USA- Born in Leningrad, Russia

- Fluent in Russian (native) and English languages
- Member of AMS

- Ph.D. in Mathematics, August 2004

University of Texas at Austin

Advisor:Prof. J. D. Vaaler

Thesis: Algebraic points of small height with additional arithmetic conditions

- B.S. in Applied Mathematics with Specialization in Computing, 1995

University of California at Los Angeles

- Professor, Claremont McKenna College, May 2015 - present

- Chair of the Department of Mathematical Sciences, Claremont
McKenna College, July 2012 - July 2014

- Associate Professor (with tenure), Claremont McKenna College,
December 2009 - May 2015

- Member of Extended Graduate Faculty, Claremont Graduate University, July 2007 - present
- Assistant Professor, Claremont McKenna College, July 2007 -
December 2009

- Visiting Assistant Professor, Texas A&M University,
September 2004 - August 2007

- Assistant Instructor and Teaching Assistant, University of
Texas at Austin, September 1998 - August 2004

- Teaching Assistant, University of Nebraska at Lincoln, Spring
1998

- Software Engineer, IBM, General Magic, Compuware, and Compaq corporations, 1995 - 1998

- Oberwolfach Research Institute for Mathematics, Research in
Pairs Program, July/August 2017

- Erwin Schrödinger International Institute for Mathematical
Physics, Vienna, Austria, October/November 2014

- Institut Mittag-Leffler (IML), Djursholm, Sweden, July/August
2013

- Max Planck Institut für Mathematik (MPIM), Bonn, Germany, July 2012
- Institut des Hautes Etudes Scientifique (IHES),
Bures-sur-Yvette, France, October/November 2010

- Max Planck Institut für Mathematik (MPIM), Bonn, Germany, June 2008
- Institut des Hautes Etudes Scientifique (IHES),
Bures-sur-Yvette, France, July 2007

- Max Planck Institut für Mathematik (MPIM), Bonn, Germany, July/August 2006

- ETH Zürich, Switzerland, 1 week in October 2018

- ETH Zürich, Switzerland, 1 week in November 2014

- Wesleyan University, Middletown, CT, USA, 1 week in July 2011
- Nanyang Technological University, Singapore, 2 weeks in May 2009
- Wesleyan University, Middletown, CT, USA, 2 weeks in July/August 2008

Number theory, arithmetic geometry, discrete and convex geometry, in particular:

- Diophantine approximation, equations, and problems
- Classical and adelic geometry of numbers
- Quadratic and linear forms; polynomials

- Theory of height functions, rational points on varieties, Mahler's measure, and connections with arithmetic geometry
- Geometric combinatorics, lattice point counting, Erhart polynomial
- Lattices, packings and coverings, linear Diophantine problem
of Frobenius

__Small zeros of quadratic forms with linear conditions__, Journal of Number Theory, vol. 108 no. 1 (2004), pg. 29-43- Lattice points in
homogeneously expanding compact domains, One section of
the omnibus Problems Article "Problems from the Cottonwood Room"
(M. Beck, B. Chen, L. Fukshansky, C. Haase, A. Knutson, B.
Reznick, S. Robins, A. Schuermann),
*Contemporary Mathematics*374 (2005), 179-191, Proceedings of the Summer 2003 AMS/MAA/SIAM Conference on Integer Points in Polyhedra

- Integral points of small height outside of a hypersurface, Monatshefte für Mathematik, vol. 147 no. 1 (2006), pg. 25-41
- Siegel's lemma with additional conditions, Journal of Number Theory, vol. 120 no. 1 (2006), pg. 13-25
- (with Sinai Robins) Frobenius problem and the covering radius of a lattice, Discrete and Computational Geometry, vol. 37 no. 3 (2007), pg. 471-483
- On effective Witt decomposition and Cartan-Dieudonné theorem, Canadian Journal of Mathematics, vol. 59 no. 6 (2007), pg. 1284-1300
- Small zeros of
quadratic forms over the algebraic closure of Q,
*International Journal of Number Theory*, vol. 4 no. 3 (2008), pg. 503-523 - On distribution of well-rounded sublattices of Z^2, Journal of Number Theory, vol. 128 no. 8 (2008), pg. 2359-2393
- On similarity classes of well-rounded sublattices of Z^2, Journal of Number Theory, vol. 129 no. 10 (2009), pg. 2530-2556
- Search bounds for zeros of polynomials over the algebraic closure of Q, Rocky Mountain Journal of Mathematics, vol. 39, no. 3 (2009), pg. 789-804
- Effective structure theorems for symplectic spaces via height, in "Quadratic forms -- algebra, arithmetic, and geometry" (R. Baeza, W.K. Chan, D.W. Hoffmann, and R. Schulze-Pillot, eds.), Contemporary Mathematics 493 (2009), pg. 117--130
- Integral orthogonal
bases of small height for real polynomial spaces, Online Journal of Analytic
Combinatorics, vol. 4 (2009), art. 7, 10 pp.

- (with Wai Kiu Chan) Small zeros of hermitian forms over quaternion algebras, Acta Arithmetica, vol. 142 no. 3 (2010), pg. 251--266
- Algebraic points of small height missing a union of varieties, Journal of Number Theory, vol. 130 no. 10 (2010), pg. 2099--2118 -- an earlier version of this paper also appears in the MPIM Preprint Series
- (with D. Moore, A. Ohana, W. Zeldow) On well-rounded sublattices of the hexagonal lattice, Discrete Mathematics, vol. 310 no. 23 (2010), pg. 3287--3302
- Revisiting the hexagonal lattice: on optimal lattice circle packing, Elemente der Mathematik, vol. 66 no. 1 (2011) pg. 1--9
- (with Sinai Robins) Bounds
for
solid angles of lattices of rank three, Journal of Combinatorial Theory A,
vol. 118 no. 2 (2011), pg. 690--701

- (with Achill Schuermann) Bounds on generalized Frobenius numbers, European Journal of Combinatorics, vol. 32 no. 3 (2011) pg. 361--368
- (with Kate Petersen) On well-rounded ideal lattices, International Journal of Number Theory, vol. 8 no. 1 (2012) pg. 189--206
- (with G. Henshaw, P. Liao, M. Prince, X. Sun, S. Whitehead) On integral well-rounded
lattices in the plane, Discrete and Computational Geometry, vol. 48
no. 3 (2012), pg. 735--748

- (with Iskander Aliev and Martin Henk) Generalized Frobenius numbers: bounds and average behavior, Acta Arithmetica, vol. 155 no. 1 (2012), pg. 53--62
- (with G. Henshaw, P. Liao, M. Prince, X. Sun, S. Whitehead) On well-rounded ideal lattices - II, International Journal of Number Theory, vol. 9 no. 1 (2013) pg. 139--154
- Heights and
quadratic forms: on Cassels' theorem and its generalizations,
in "Diophantine methods, lattices, and arithmetic theory of
quadratic forms" (W. K. Chan, L. Fukshansky, R. Schulze-Pillot,
and J. D. Vaaler, eds.), Contemporary
Mathematics, AMS vol. 587 (2013), pg. 77--94

- (with Glenn Henshaw) Lattice point counting and height bounds over number fields and quaternion algebras, Online Journal of Analytic Combinatorics, vol. 8 (2013), art. 4, 20 pp.
- Well-rounded
zeta-function of planar arithmetic lattices, Proceedings of the American
Mathematical Society, vol. 142 no. 2 (2014), pg.
369--380

- (with Wai Kiu Chan and Glenn Henshaw) Small zeros of quadratic forms missing a union of varieties, Transactions of the AMS, vol. 366 no. 10 (2014), pg. 5587--5612
- (with Hiren Maharaj) Lattices from elliptic curves over finite fields,
Finite Fields and Their
Applications, vol. 28 (July 2014), pg. 67--78

- (with Xun Sun) On the geometry of cyclic lattices, Discrete and Computational Geometry, vol. 52 no. 2 (2014), pg. 240--259
- Stability of ideal lattices from quadratic number fields, The Ramanujan Journal, vol. 37 no. 2 (2015), pg. 243--256
- (with Albrecht Boettcher, Stephan Garcia, and Hiren Maharaj) Toeplitz determinants with
perturbations in the corners, Journal of Functional Analysis, vol. 268 no. 1
(2015), pg. 171--193

- (with Albrecht Boettcher, Stephan Garcia, and Hiren Maharaj) On lattices generated by
finite Abelian groups, SIAM Journal on Discrete Mathematics, vol. 29
no. 1 (2015), pg. 382--404

- (with Stephan Garcia and Xun Sun) Permutation invariant lattices, Discrete Mathematics, vol. 338 no. 8 (2015), pg. 1536--1541
- Height bounds on zeros of quadratic forms over Q-bar, Research in Mathematical Sciences, vol. 2 no. 1 (2015), art. 19, 26 pp.
- (with Wai Kiu Chan and Glenn Henshaw) Totally isotropic
subspaces of small height in quadratic spaces, Advances in Geometry, vol.
16 no. 2 (2016), pg. 153--164

- (with Albrecht Boettcher, Stephan Garcia, and Hiren Maharaj) Lattices from Hermitian
function fields,
*Journal of Algebra*, vol. 447 (2016), pg. 560--579 - (with Albrecht Boettcher, Stephan Garcia, Hiren Maharaj, and
Deanna Needell) Lattices
from tight equiangular frames,
*Linear Algebra and its Applications*, vol. 510 (2016), pg. 395--420 - (with Albrecht Boettcher, Stephan Garcia, and Hiren Maharaj) Lattices from Abelian
groups, in "Lattices and Applications in Number
Theory,"
*Oberwolfach Reports*, vol. 13 no. 1 (2016), pg. 87--154

- (with Pavel Guerzhoy and Florian Luca)
__On arithmetic lattices in the plane__, Proceedings of the American Mathematical Society, vol. 145 no. 4 (2017), pg. 1453--1465 - (with Albrecht Boettcher) Addendum to: Lattices from tight equiangular frames,
*Linear Algebra and its Applications*, vol. 531 (2017), pg. 592--601

- (with Albrecht Boettcher, Stephan Garcia, and Hiren Maharaj) Lattice theory and
Toeplitz determinants,
*Operator Theory: Advances and Applications*, vol. 262 (2018), pg. 117--138

- (with Adib Shaar)
__A new family of one-coincidence sets of sequences with dispersed elements for frequency hopping CDMA systems__,*Advances in Mathematics of Communications*, vol. 12 no. 1 (2018), pg. 181--188

- (with Nikolay Moshchevitin)
__On an effective variation of Kronecker's approximation theorem avoiding algebraic sets__, Proceedings of the American Mathematical Society, vol. 146 no. 10 (2018), pg. 4151--4163 -- an extended version of this paper (also joint with O. German) appears in the Oberwolfach preprint series - (with Deanna Needell and Benny Sudakov) An algebraic perspective
on integer sparse recovery,
*Applied Mathematics and Computation*, vol. 340 (2019), pg. 31--42 - (with Albrecht Boettcher, Simon Eisenbarth, Stephan Garcia, and Hiren Maharaj) Spherical 2-designs and lattices from Abelian groups, Discrete and Computational Geometry, vol. 61 no. 1 (2019) pg. 123--135
- (with Wai Kiu Chan) Small representations of integers by integral quadratic forms, Journal of Number Theory, vol. 201 (2019) pg. 40--52
- (with Taoufiq Damir)
__Canonical basis twists of ideal lattices from real quadratic number fields__, Houston Journal of Mathematics, vol. 45 no. 4 (2019) pg. 999--1019 - (with Deanna Needell, Josiah Park and Jessie Xin) Lattices from tight frames
and vertex transitive graphs, Electronic Journal of Combinatorics, vol. 26
no. 3 (2019), P3.49, 30 pp.

- (with Ed Shi) Positive semigroups and generalized Frobenius numbers over totally real number fields, Moscow Journal of Combinatorics and Number Theory, vol. 9 no. 1 (2020) pg. 29--41
- (with Soren Aletheia-Zomlefer and Stephan Garcia)
__The Bateman-Horn conjecture: Heuristic, history, and applications__, Expositiones Mathematicae, vol. 38 no. 4 (2020), pg. 430--479 - (with Albrecht Boettcher) Representing integers by multilinear polynomials, Research in Number Theory, vol. 6 no. 4 (2020), Article #38
- (with Alex Hsu) Covering point-sets with parallel hyperplanes and sparse signal recovery, submitted for publication
- (with David Kogan)
__On the geometry of nearly orthogonal lattices__,*Linear Algebra and its Applications,*vol. 629 (2021), pg. 112--137

- (with Pavel Guerzhoy and Stefan Kuehnlein)
__On sparse geometry of numbers__,*Research in the Mathematical Sciences*, vol. 8 no. 1 (2021), Article #2 - (with Maxwell Forst)
__Counting basis extensions in a lattice__, submitted for publication - (with David Kogan)
__On average coherence of cyclotomic lattices__, to appear in*Communications in Mathematics* - (with Siki Wang)
__Positive semigroups in lattices and totally real number fields__, to appear in*Advances in Geometry* - (with David Kogan)
__Cyclic and well-rounded lattices__, submitted for publication

Book

- (with Stephan Garcia)
__Geometric Number Theory__, under contract with*Cambridge University Press*

Editorial

- Chebyshevskii Sbornik, an editor (2019 - present)

- Online Journal of Analytic Combinatorics, an editor (2013 -
present)

- "Diophantine methods, lattices, and arithmetic theory of
quadratic forms" -- proceedings of a BIRS workshop (Editors: W.
K. Chan, L. Fukshansky, R. Schulze-Pillot, J. D. Vaaler), Contemporary Mathematics,
AMS vol. 587 (2013)

- Convocation Speaker, Claremont McKenna College, September 2018

- Simons Foundation Collaboration Grant for Mathematicians, 2017-2022
- National Security Agency, Young Investigator Grant, 3/2015 - 3/2017
- Simons Foundation Collaboration Grant for Mathematicians, 2013-2018 (terminated in 2015 due to NSA grant)
- National Security Agency, Young Investigator Grant, 2/2012 -
2/2014

- Simons Foundation Collaboration Grant for Mathematicians,
2011-2016 (terminated in 2012 due to NSA grant)

- Number Theory Foundation conference grant: travel support for
the junior participants of a BIRS workshop, November 2011

- Faculty Research Grants, Claremont McKenna College, multiple
awards 2008 - present

- Senior personnel on NSF grant DMS-0755540: REU program for
Claremont Colleges, 2008-2011

- Teaching Resource Center mini-grant, Claremont McKenna
College, Spring 2008

- AMS/NSF travel grant for ICM 2006, August 2006

- NSF VIGRE postdoctoral fellowship, Texas A&M University,
2004-2005

- Graduate Research Assistanship, University of Texas at Austin, Summer 2002
- NSF VIGRE traveling support, University of Texas at Austin,
December 2001

- Dodd Teaching Excellence Award, Department of Mathematics, University of Texas at Austin, 2000
- First year summer fellowship, Department of Mathematics, University of Texas at Austin, 1999
- CalGrant Scholarship, University Scholarship, and College of Letters and Science Honors, UCLA, 1992-1993

- Representing
integers by multilinear polynomials, Selected
Topics in Mathematics online seminar, University of
Liverpool, UK (October 29, 2021)

- On sparse geometry
of numbers, Diophantine Analysis and Related Topics,
online conference at Moscow State University, Russia (May 31 -
June 5, 2021)

- Representing integers by multilinear polynomials, Diophantine Analysis online seminar, Moscow State University, Russia (April 8, 2021)
__Lattices from group frames and vertex transitive graphs__, Algebra Seminar, Florida State University, Tallahassee, Florida (November 20, 2019)- Heights and quadratic forms, Colloquium, University of Texas Rio Grande Valley, Edinburg, Texas (November 19, 2019)
__Lattices from group frames and vertex transitive graphs__, Combinatorics Seminar, University of Texas Rio Grande Valley, Brownsville, Texas (November 18, 2019)__Bounds on linear forms and integer sparse recovery__, Baikal Number Theory Conference, Olkhon Island, Russia (August 26 - 30, 2019)

__Lattices from group frames and vertex transitive graphs__, Number Theory Seminar, Moscow State University, Russia (August 23, 2019)__Lattices from group frames and vertex transitive graphs__, Southern Illinois University Conference on Pure Mathematics, Carbondale, IL (May 14 - 16, 2019)__An algebraic perspective on integer sparse recovery__, Combinatorics Seminar, UCLA, (May 9, 2019)

- Bounding linear
forms on a lattice away from zero, Conference on
the Arithmetic Theory of Quadratic Forms, Seoul National
University (January 7 - 11, 2019)

- Small representations of integers by integral quadratic forms, Algebra, Number Theory, and Discrete Mathematics Seminar, Cal State Northridge (November 14, 2018)
__An algebraic perspective on integer sparse recovery__, Combinatorics Seminar, USC, Los Angeles, CA (October 31, 2018)__An algebraic perspective on integer sparse recovery__, Theory of Combinatorial Algorithms Seminar, ETH Zurich, Zurich, Switzerland (October 25, 2018)

- Lattices generated by equiangular tight frames, Workshop on Computational Challenges in the Theory of Lattices, ICERM Brown (April 23 - 27, 2018)
__An effective variation of Kronecker's approximation theorem__, AMS Special Session:*A Showcase of Number Theory at Liberal Arts Colleges*, San Diego, CA (January 10 - 11, 2018)__On some algebraic lattice constructions__, Number Theory Seminar, Texas A&M University, College Station, TX (September 8, 2017)

__Solving systems of quadratic equations over Q-bar__, AMS Special Session:*Numbers, Functions, Transcendence and Geometry*, Denton, TX (September 9 - 10, 2017)

__On two constructions of extremal lattices__, Vilnius Conference in Combinatorics and Number Theory, Vilnius, Lithuania (July 17 - 22, 2017)

- Lattices generated
by equiangular tight frames, Combinatorics Seminar,
UCLA, (June 1, 2017)

__On some algebraic constructions of extremal lattices__, Combinatorics Seminar, Caltech (February 22, 2017)__On some algebraic constructions of extremal lattices__, Number Theory Seminar, UC Irvine (October 18, 2016)

__Lattices from Abelian groups, spherical designs, and packing density maxima__, Operations Research Seminar, Cardiff University, Cardiff, UK (July 13, 2016)

__Generalized Frobenius numbers: bounds and average behavior via geometric techniques__, International meeting on numerical semigroups with applications, Levico Terme, Italy (July 4 - 8, 2016)

- Well-rounded
lattices from algebraic constructions, Sabanci
University, Istanbul, Turkey (June 8, 2016)

- Well-rounded
lattices from algebraic constructions, ANTA Seminar,
Aalto University, Helsinki, Finland (June 5, 2016)

__On arithmetic lattices in the plane__, Southern Illinois University Conference on Pure Mathematics, Carbondale, IL (May 15 - 17, 2016)

__On lattices generated by finite Abelian groups__, Southern California Discrete Math Symposium 2016, UCLA, April 16, 2016

__Lattices from Abelian groups__, Workshop on "Lattices and Applications in Number Theory", Oberwolfach, Germany (January 17 - 23, 2016)

- Height bounds for
zeros of quadratic forms, Diophantine Approximation and
Related Topics, Aahrus, Denmark (July 13 - 17, 2015)

- Solving quadratic
equations over Q-bar, Algebra, Number Theory, and
Discrete Mathematics Seminar, Cal State Northridge (April 29,
2015)

- Height bounds on
zeros of quadratic forms over Q-bar, AMS Special
Session: Quadratic Forms in
Arithmetic and Geometry, AMS Spring Western Section
Meeting, Huntsville, AL, March 2015

- Searching for rational points on varieties over global fields, University of Göttingen, Germany (November 16-22, 2014)
- On the Frobenius problem and its generalization, Theory of Combinatorial Algorithms Seminar, ETH Zürich, Switzerland, November 11, 2014
- Well-rounded
lattices from algebraic constructions, TU Berlin,
November 5, 2014

- Well-rounded
lattices from algebraic constructions, plenary lecture
at the Workshop on
"Sphere Packings, Lattices, and Designs", Program on "Minimal Energy
Point Sets, Lattices, and Designs", Erwin Schrödinger
International Institute for Mathematical Physics,
Vienna, Austria (October 27-31, 2014)

- On stability of
ideal lattices from quadratic number fields, ICM 2014
Satellite Conference on Integral Quadratic Forms and Related
Topics, Gyeongju, South Korea (August 7-11, 2014)

- Computational
complexity of lattice problems and cyclic lattices,
2014 Undergraduate Summer Research Program Polygons and
Polynomials, ICERM - Brown University, July 28, 2014

- Heights and
effective theory of quadratic forms over global fields,
University of Colorado at Boulder, Number Theory seminar,
Boulder, Colorado (April 3, 2014)

- Well-rounded
lattices from algebraic constructions, International
Conference on The Algebraic and Arithmetic Theory of Quadratic
Forms 2013, Puerto Natales, Patagonia, Chile (December 16-21,
2013)

- Computational
complexity of lattice problems and cyclic lattices, Colloquium,
California State University Dominguez Hills, October 2013

- Complexity of
lattice problems on cyclic lattices, Combinatorics
Seminar, UCLA, February 2013

- On the geometry of cyclic lattices, Algebra and Discrete Mathematics Seminar, UC Davis, Davis, CA, February 2013
- Computational complexity of lattice problems and cyclic lattices, Graduate Seminar, California State University Channel Islands, Camarillo, CA, February 2013
- On integral well-rounded lattices, Number Theory Seminar, Max Planck Institut für Mathematik, Bonn, Germany, July 2012
- On integral
well-rounded lattices, Mathematics Colloquium,
Karlsruhe Institute of Technology, Karlsruhe, Germany, July 2012

- On the Frobenius
problem and its generalization, Number Theory Seminar,
Universitaet des Saarlandes, Saarbruecken, Germany, July 2012

- On minimal lattice
spherical configurations in three dimensions, Analysis
Seminar, California State University Fullerton, April 2012

- Search bounds with
respect to height in linear and quadratic spaces,
Minisymposium: Arithmetic
aspects of numerical solving at the SIAM Conference on
Applied Algebraic Geometry, North Carolina State University,
Raleigh, North Carolina (October 6-9, 2011)

- On the Frobenius
problem and its generalization, Colloquium,
California State University Dominguez Hills, September 2011

- On minimal lattice
spherical configurations in three dimensions,
Combinatorics Seminar, UCLA, May 2011

- On distribution of integral well-rounded lattices in the plane, Special Session: Arithmetic of quadratic forms and integral lattices at the First Joint Meeting of AMS and Sociedad Mathematica de Chile, Pucon, Chile (December 15-18, 2010)
- Heights and effective theory of quadratic forms over global fields, Workshop on the arithmetic of quadratic forms and integral lattices, Lake Ranco, Chile (December 13-14, 2010)
- Searching for
rational points on varieties over global fields, Colloquium,
Uppsala University, November 2010

- On Siegel's lemma
outside of a union of varieties, Oberseminar des
Institutes für Algebra und Geometrie, University of Magdeburg,
November 2010

- On the Frobenius problem and its generalization, Colloquium, University of Rostock, November 2010
- Small zeros of hermitian forms over quaternion algebras, Number Theory Seminar, Institut de Mathématiques de Jussieu, Paris, France, October 2010
- On the Frobenius
problem and covering radius of a lattice, Combinatorics
Seminar, UCLA, May 2010

- On distribution of
well-rounded lattices in the plane, Number Theory
Seminar, UC Irvine, March 2010

- Small zeros of
hermitian forms over quaternion algebras, AMS-KMS
Special Session: Arithmetic
of quadratic forms, First Joint Meeting of AMS and
Korean Mathematical Society, Seoul, South Korea (December 16-20,
2009) -- CANCELLED

- On the Frobenius
coin-exchange problem, Graduate Seminar, California
State University Channel Islands, Camarillo, CA, September 2009

- Points of small
height missing a union of varieties, AMS Special
Session: Algebra and Number
Theory with Polyhedra, AMS Spring Western Section
Meeting, San Francisco, CA, February 2009

- Siegel's lemma
outside of a union of varieties, AMS Special Session: Number Theory, AMS Fall
Eastern Section Meeting, Middletown, CT, October 2008

- On distribution of
well-rounded sublattices of Z^2, Séminaire de Théorie
des Nombres, Institut de Mathématiques de Bordeaux, University
of Bordeaux, France, June 2008

- On similarity
classes of well-rounded sublattices of Z^2, Oberseminar
des Institutes für Algebra und Geometrie, University of
Magdeburg, Germany, June 2008

- On zeta
function of well-rounded sublattices of Z^2,
Number Theory Seminar, Institut de Mathématiques de Jussieu,
Paris, France, May 2008

- Sphere packing,
lattices, and Epstein zeta function, Colloquium,
California State University at Los Angeles, April 2008

- Sphere packing,
lattices, and Epstein zeta function, Colloquium,
California State University at Northridge, March 2008

- Frobenius number,
covering radius, and well-rounded lattices, AMS Special
Session:
*The linear Diophantine problem of Frobenius*, Joint Mathematics Meeting, San Diego, CA, January 2008

- Effective structure
theorems for quadratic spaces via height, Second
International Conference on The Algebraic and Arithmetic Theory
of Quadratic Forms 2007, Lake Llanquihue, Chile, December 2007

- Sphere packing,
lattices, and Epstein zeta function, Claremont
Mathematics Colloquium, Claremont Colleges, November 2007

- Effective theorems
for quadratic spaces via height, Number Theory Seminar,
UCLA, October 2007

- Frobenius number,
covering radius, and well-rounded lattices, Colloquium,
George Mason University, February 2007

- Frobenius number, covering radius, and well-rounded lattices, Colloquium, Bucknell University, February 2007
- Frobenius number,
covering radius, and well-rounded lattices, Colloquium,
Claremont McKenna College, January 2007

- Effective
decompositions of quadratic spaces via heights, Number
Theory Seminar, Max Planck Institut für Mathematik - Bonn, July
2006

- Frobenius number,
covering radius, and ESM lattices, Number Theory
Seminar, University of Göttingen, June 2006

- Quadratic forms and
height functions, Colloquium of the Graduiertenkolleg,
University of Göttingen, June 2006

- On the linear
Diophantine problem of Frobenius, Oberseminar des
Institutes für Algebra und Geometrie , University of Magdeburg,
June 2006

- On the Frobenius
problem, Algebra-Geometry-Combinatorics Seminar, San
Francisco State University, May 2006

- Frobenius number of
ESM lattices, Number Theory Seminar, University of
Texas at Austin, February 2006

- The Frobenius
problem and the covering radius of a lattice,
Colloquium, Temple University, February 2006

- Effective theorems
for quadratic spaces over the algebraic closure of Q, AMS
Special Session on Mahler Measure and Heights, Joint Mathematics
Meeting, San Antonio, TX, January 2006

- Effective structure
theorems for quadratic spaces and their isometries,
Number Theory Seminar, University of Illinois at
Urbana-Champaign, February 2005

- Heights and Diophantine problems, Colloquium, Rice University, September 2004
- Small zeros of quadratic polynomials, Number Theory Seminar, Texas A&M University, November 2003
__Small zeros of quadratic forms with linear conditions__, Mahler's Measure of Polynomials Conference, Simon Fraser University, June 2003

- On sparse geometry
of numbers, AustMS 2020 Meeting Online, Special Session
on Number Theory and Algebraic Geometry, December 2020

- Orthogonal Siegel's
lemma, Illinois Number Theory Conference, May 2010

- Algebraic points of
small height missing a union of varieties, Western
Number Theory Conference, Fort Collins, CO, December 2008

- Siegel's lemma
outside of a union of varieties, Number Theory Seminar,
UCLA, November 2008

- On distribution of
well-rounded sublattices of Z^2, CNTA10, Waterloo,
Canada, July 2008

- Effective theorems
for quadratic spaces via height, Seminaire de theorie
des nombres de Chevaleret,
Institut de Mathématiques de Jussieu, Paris,
France, July 2007

- On distribution of
integral well-rounded lattices in dimension two,
Illinois Number Theory Fest, May 2007

- Effective theorems
for quadratic spaces, ICM 2006, Madrid, Spain, August
2006

- Frobenius problem
and the covering radius of a lattice, West Coast Number
Theory, Pacific Grove, CA, December 2005

- Some effective
Diophantine results over the algebraic closure
of Q,
XXIVth Journées Arithmétiques, Marseilles, France, July 2005

- Effective
decompositions of quadratic spaces, ArithmeTexas,
College Station, TX, April 2005

- Counting lattice
points in admissible adelic sets, MNTCG2,
Urbana-Champaign, IL, February 2005

__On effective Witt decomposition__and Cartan-Dieudonné theorem, West Coast Number Theory Conference, Las Vegas, NV, December 2004

- Siegel's lemma with additional conditions, CNTA8, Toronto, June 2004
- Integral points of small height outside of a hypersurface, Illinois Number Theory Conference, Urbana-Champaign, May 2004
- Lattice points of small height in projective varieties, Integer points in polyhedra, Joint Summer research conferences, Snowbird, Utah, July 2003
__On a discrete analogue of the Tarski plank problem__, West Coast Number Theory Conference, SFSU, San Francisco, December 2002- Points of small
height outside of a collection of subspaces
*,*CNTA7, Montreal, Canada, May 2002 __Small zeros of quadratic forms over a number field__, West Coast Number Theory Conference, Pacific Grove, CA, December 2001

- A difference in
numbers, keynote lecture for the Center for Talented
Youth Science and Technology event at Claremont McKenna College,
October 2018

- The makings of a
good problem: theory and applications, keynote address
at the 72nd Annual Convocation, Claremont McKenna College,
September 2018

- A difference in
numbers, invited lecture at GEMS: Gateway to Exploring
Mathematical Sciences, Claremont Colleges, November 2017

__How to count to infinity: a combinatorial approach to geometry__, a break-out session for the Center for Talented Youth Science and Technology event at Claremont McKenna College, March 2017

__How to count to infinity: a combinatorial approach to geometry__, a break-out session for the Center for Talented Youth Science and Technology event at Claremont McKenna College, October 2015

- Math for the New
Millennium: Ideas that Change the World, a panel
presentation at the Marian Miner Cook Athenaeum, Claremont
McKenna College (joint with A. Aksoy, B. Hunter, and C.-Y. Kao),
October 2015

- A Challenge for the
Millennium: the Million Dollar Problems in Mathematics,
a panel presentation at the Marian Miner Cook Athenaeum,
Claremont McKenna College (joint with M. Huber, D. Needel, and
S. Nelson), April 2013

- The kissing number
problem: from Newton and Gauss to the present day, a
lecture in the Claremont McKenna College Math Club, March 2013

- Math in the grocery
aisle: from stacking oranges to constructing error-correcting
codes, invited lecture at GEMS: Gateway to Exploring
Mathematical Sciences, Claremont Colleges, February 2009

- Mahler's measure and
Lehmer's conjecture, Mathematics Graduate Student
Organization Seminar, Texas A&M University, October 2006

- Packing oranges and
constructing error correcting codes, invited lecture to
school students as a part of Math Awareness Month, Texas A&M
University, April 2006

- Simultaneous
Diophantine approximations and a conjecture of Minkowski,
Introduction to Mathematical Research seminar series, University
of Texas at Austin, March 2006

- Semester review of
calculus, invited lecture to freshmen engineering
students as a part of Texas A&M Leaders in Freshman
Engineering final review series, December 2005

- Diophantine
equations: the mystery of numbers, invited lecture to
high school students as a part of Texas A&M Summer Honors
Invitational Program (SHIP), June 2005

- Representing
integers by multilinear polynomials, Algebra / Number
Theory / Combinatorics Seminar, Claremont Colleges, September
2021

- Covering point-sets with parallel hyperplanes and sparse signal recovery, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, February 2020
__Frobenius problem over number fields__, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, September 2019__Lattices from group frames and vertex transitive graphs__, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, February 2019

- Algebraic approach to integer sparse recovery, Claremont Mathematics Weekend, January 2019
__Digital sequences for frequency hopping CDMA systems__, Applied Mathematics Seminar, Claremont Colleges, November 2018

__Small representations of integers by integral quadratic forms__, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, September 2018

__An algebraic perspective on integer sparse recovery__, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, October 2017__Counting arithmetic lattices in the plane__, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, February 2017- Constructing extremal lattices in Euclidean spaces, Claremont Mathematics Colloquium, Claremont Colleges, February 2017
__Some arithmetic constructions with equiangular frames__, Claremont Mathematics Weekend, January 2017__On effective variations of Kronecker's approximation theorem__, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, February 2016__Arithmetic lattices and elliptic curves__, Claremont Mathematics Weekend, January 2016

__Optimization problems on planar lattice transmitter networks__, Applied Mathematics Seminar, Claremont Colleges, October 2015

- Solving quadratic
equations over Q-bar, Algebra / Number Theory /
Combinatorics Seminar, Claremont Colleges, September 2015

- On the Frobenius problem and its generalization, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, October 2014
- Well-rounded lattices from algebraic constructions, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, September 2014
- Automorphism groups
of lattices, Minkowski reduction domain, and well-rounded
retract, Algebra / Number Theory / Combinatorics
Seminar, Claremont Colleges, April 2014

- Searching for
rational points on varieties over global fields,
Claremont Mathematics Colloquium, Claremont Colleges, February
2014

- On stability of
ideal lattices from quadratic number fields, Algebra /
Number Theory / Combinatorics Seminar, Claremont Colleges,
November 2013

- Complexity of
lattice problems on cyclic lattices, Algebra / Number
Theory / Combinatorics Seminar, Claremont Colleges, April 2013

- On a counting
problem in number theory, Algebra / Number Theory /
Combinatorics Seminar, Claremont Colleges, October 2012

- On zeta-function of
well-rounded lattices in the plane, Analysis Seminar,
Claremont Colleges, February 2012

- Lattices must be fat -- no skinny lattice for you!, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, February 2012
- Integer knapsacks
and the Frobenius problem, Statistics / Operations
Research / Math Finance seminar, Claremont Colleges, April 2011

- On well-rounded
ideal lattices, Algebra / Number Theory / Combinatorics
Seminar, Claremont Colleges, January 2011

- Revisiting the
hexagonal lattice: on optimal lattice circle packing,
Algebra / Number Theory / Combinatorics Seminar, Claremont
Colleges, February 2010

- On minimal lattice
spherical configurations in three dimensions, Topology
and Geometry seminar, Claremont Colleges, November 2009

- Diophantine
approximation on a circle, Analysis Seminar, Claremont
Colleges, April 2009

- On heights of
algebraic numbers, Algebra / Number Theory /
Combinatorics Seminar, Claremont Colleges, March 2009

- On Tarski plank
problem and its discrete analogues, Analysis Seminar,
Claremont Colleges, November 2008

- On Siegel's lemma, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, September 2008
- On distribution of well-rounded sublattices of Z^2, Analysis Seminar, Claremont Colleges, September 2008
- Mahler's measure, Lehmer's conjecture, and some connections - II, Analysis Seminar, Claremont Colleges, April 2008
- Mahler's measure,
Lehmer's conjecture, and some connections - I, Analysis Seminar,
Claremont Colleges, February 2008

- On zeta function of
well-rounded lattices, Analysis Seminar, Claremont
Colleges, November 2007

- Hilbert's 10-th
problem, heights, and search bounds for rational points on
varieties, Parts I and II, Algebra / Number Theory /
Combinatorics Seminar, Claremont Colleges, September 2007

- On the distribution
of integral well-rounded lattices in dimension two, Part II,
Number Theory Seminar, Texas A&M University, February 2007

- On the distribution
of integral well-rounded lattices in dimension two, Part I,
Number Theory Seminar, Texas A&M University, September 2006

- Effective theorems
for quadratic spaces over Q-bar, Number Theory Seminar,
Texas A&M University, January 2006

- The Frobenius
problem and the covering radius of a lattice, Number
Theory Seminar, Texas A&M University, October 2005

- Some effective
Diophantine results over Q-bar
*,*Number Theory Seminar, Texas A&M University, April 2005

- On effective Witt
decomposition and Cartan-Dieudonné theorem, Number
Theory Seminar, Texas A&M University, September 2004

- Points of small height with arithmetic conditions, Number Theory Seminar, University of Texas at Austin, November 2003

- Arizona Winter School: Special Functions and Transcendence, Tucson, AZ, March 2008
- SMS-NATO ASI 2005: Equidistribution
in Number Theory, Montreal, Canada, July 2005

- Arizona Winter School: Number Theory and Physics, Austin, TX, March 2004
- NSF-CBMS Special Program:
*Web of Modularity*, Urbana, IL, June 2003 - MSRI Summer Program:
*Excursions in Computational Number Theory - Polynomials with integer coefficients*, Vancouver, Canada, June 2002;__Project and presentation__:*Heights of products of cyclotomic polynomials* - Illinois Number Theory Conference, Urbana, IL, May 2002
- Arizona Winter School:
*Periods*, Tucson, AZ, March 2002

Postdoctoral
fellows supervision

- David Krumm (at Claremont McKenna College), 2013 - 2015

Ph.D.
students

- Glenn Henshaw, (joint with Wai Kiu Chan) Ph.D. from Wesleyan University, May 2012
- Xun Sun, Ph.D. from Claremont Graduate University, May 2015
- David Kogan, Ph.D. in progress at Claremont Graduate University
- Maxwell Forst, Ph.D. in progress at Claremont Graduate University

Ph.D.
and M.S. thesis committee service

- Member of the Ph.D. Dissertation Committee for Ahmed Al Fares, Claremont Graduate University
- External Examiner for Jose Miguel Cruz's M.S. Thesis (Universidad de los Andes, M.S. July 2020)
- External Examiner for Santiago Cortes Gomez's M.S. Thesis
(Universidad de los Andes, M.S. May 2018)

- External Examiner for Dilbak Mohammed's Ph.D. Dissertation
(Cardiff University, Ph.D. December 2016)

- Gutachter/Expert Referee for Carsten Thiel's Ph.D. Dissertation (University of Magdeburg, Ph.D. February 2014)
- External Member of the Ph.D. Dissertation Committee for Nikolas Rauh (University of Texas at Austin, Ph.D. May 2013)
- External Member of the Ph.D. Dissertation Committee for Mark Rothlisberger (University of Texas at Austin, 2010)

Undergraduate
thesis and research supervision

- Advisor for senior thesis student Siki Wang (Claremont McKenna College, B.A. expected May 2022, Best Thesis Award)
- Advisor for summer research and senior thesis student Yingqi (Ed) Shi (Claremont McKenna College, B.A. May 2020, Outstanding Math Major Award)
- Advisor for senior thesis student Alexander Hsu (Claremont McKenna College, B.A. December 2019, Best Thesis Award and Outstanding Math Major Award)
- Advisor for senior thesis student Yuxin (Jessie) Xin (Claremont McKenna College, B.A. May 2019)
- Advisor for senior thesis student Scott Maislin (Claremont McKenna College, B.A. May 2017)
- Advisor for senior thesis student Mia Siracusa (Scripps College, B.A. May 2017)
- Advisor for senior thesis student Michelle Goodwin (Claremont McKenna College, B.A. May 2016)
- Advisor for senior thesis student Emma Cranston (Scripps College, B.A. May 2016)
- Advisor for independent study students Joshua Corwin and
Christian Modjaiso (Pitzer College, Summer 2015)

- Advisor for senior thesis student Tatiana Bradley (Scripps College, B.A. May 2015)
- Advisor for senior thesis student John Shaughnessy (Claremont McKenna College, B.A. May 2014, Best Thesis Award)
- Advisor for senior thesis and research student Michael Mei (Pomona College, B.A. May 2014)
- Advisor for research student Arvind Suresh (Claremont McKenna
College, Spring and Summer 2013)

- Advisor for senior thesis student Jonathan Raiman (Pomona
College, B.A. May 2013)

- Reader for senior thesis student Amanda Clemm (Scripps College, B.A. May 2012)

Research
programs supervision

- Instructor and Project Leader for the Claremont Colleges Fletcher Jones Summer 2011 Research Program for graduate and undergraduate students, Summer 2011
- Instructor and Project Leader for an NSF-funded REU program, Claremont Colleges REU, 2009

Organizing
activities

- Member of the scientific committee for the Southern
California Discrete Mathematics Symposium, 2020 - present

- Co-organizer (with S. Assaf) of the Southern California
Discrete Mathematics Symposium 2019, Claremont, California
(May 4, 2019)

- Co-organizer (with S. Akhtari and C. Petsche) of
__AMS Special Session____:__at the Joint Mathematics Meeting - 2018, San Diego, California (January 12 - 13, 2013)*Diophantine Approximation and Analytic Number Theory in Honor of Jeffrey Vaaler* - Co-organizer (with D. Krumm) of AMS Special Session:
*Heights, Diophantine problems, and lattices*, Riverside, California (November 2-3, 2013) - Co-organizer (with W. K. Chan) of AMS Special Session:
*Arithmetic theory of quadratic forms and lattices*at the Joint Mathematics Meeting - 2013, San Diego, California (January 10, 2013) - Co-organizer (with W. K. Chan, R. Schulze-Pillot, J. D. Vaaler) of a 5-day workshop on Diophantine methods, lattices, and arithmetic theory of quadratic forms, BIRS, Banff, Canada (November 13 - 18, 2011)
- Co-organizer (with S. Garcia) for the Claremont Mathematics Colloquium, Claremont Colleges, 2011-2012
- Co-organizer (with G. Karaali) for the Algebra / Number Theory / Combinatorics seminar, Claremont Colleges, 2009-present
- Co-organizer (with M. Beck) of AMS Special Session:
*Diophantine problems and discrete geometry*, AMS Spring Western Section Meeting, Claremont, CA, May 2008 - Local organizer of AMS Spring Western Section Meeting, Claremont, CA, May 2008
- Organizer for the Number Theory seminar, Texas A&M University, 2006-2007
- Organizer for the Working Number Theory seminar, Texas A&M University, 2004 - 2005

Reviewing and refereeing
service

__Referee for the following journals__:

- Journal of Number Theory
- Canadian Mathematical Bulletin
- International Journal of Number Theory
- Mathematics of Operations Research
- Journal of Combinatorial Theory A
- Acta Arithmetica
- Proceedings of the American Mathematical Society
- Advances in Geometry
- American Mathematical Monthly
- Mathematica Bohemica
- Geometriae Dedicata
- Involve
- Electronic Journal of Combinatorics
- Proceedings of the London Mathematical Society
- Journal de Théorie des Nombres de Bordeaux
- Canadian Journal of Mathematics
- SIAM Journal on Discrete Mathematics
- Symposium on Discrete Algorithms
- Mathematics of Computation
- Alabama Journal of Mathematics
- Houston Journal of Mathematics
- Mathematical Intelligencer
- Moscow Journal of Combinatorics and Number Theory
- Communications in Mathematics
- Pacific Journal of Mathematics
- European Journal of Combinatorics
- Advances in Mathematics of Communication
- The Ramanujan Journal
- Discrete Mathematics
- Discrete and Computational Geometry
- Cryptography and Communications
- Computational and Applied Mathematics
- Linear Algebra and its Applications
- IMRN
- Designs, Codes and Cryptography
- Journal of Analysis
- Combinatorial Theory
- Integers
- Expositiones Mathematicae
- Monatshefte fur Mathematik

__Referee for the following proceedings:__- A Journey Through Discrete Mathematics
- IWOTA 2019 Proceedings

__Referee / reviewer for the following book publishers:__- Pearson Publishing
- W. H. Freeman Publishing
- Springer Developments in Mathematics Series
- Cambridge University Press
- American Mathematical Society

__Referee for the following grants and fellowships:__- National Security Agency
- Canada Council for the Arts: Killam Program
- Marie Curie Actions: Career Integration Grant program
- Davidson Fellows Scholarship program

__Reviewer for the following reviewing services:__- AMS Mathematical Reviews (MathSciNet)
- Zentralblatt MATH (zbMATH)

- Member of a Zippia expert panel on current analytic job market
trends, January 2021

- Judge for SOLVE 2019 competition of the Pasadena Unified School District Math Academy US, May 11, 2019 at CalTech
- 3rd Grade Math Circle at Chaparral Elementary School (Claremont, CA), AY 2018 - 2019
- Local organizer for Center for Talented Youth Science and Technology event at Claremont McKenna College, October 2018
- Judge for SOLVE 2018 competition of the Pasadena Unified School District Math Academy US, May 5, 2018 at CalTech
- Chaparral Elementary School Career Day presentation
(Claremont, CA), February 23, 2018

- Judge for SOLVE 2017 competition of the Pasadena Unified
School District Math Academy US, May 13, 2017 at CalTech

- Co-organizer (with D. Needell) of the CMC Math Club, 2013

- Co-organizer (with CMC Career Services) of the CMC Careers in Mathematics Event, 2012
- Co-organizer (with M. O'Neill) of the CMC 4th annual Atul Vyas
Memorial Lecture in Mathematics, 2011

- Speaker for a GEMS (Gateway to Exploring Mathematical Sciences) event for middle school students, 2009
- Co-organizer (with M. O'Neill) of Putnam preparation seminar at Claremont McKenna, 2007, 2008
- Co-organizer (with M. O'Neill) of a mathematical
problem-solving contest at Claremont McKenna, 2008

- Speaker and contest problem grader for Math Awareness event
for elementary, middle, and high school students, 2006

- Assistant Instructor for an REU/VIGRE course, 2005

- Participated in Texas A&M Summer Honors Invitational
Program (SHIP) for high school students, 2005

- Instructor for Emerging Scholars Program (ESP), 2001-2002
- Instructor for Supplemental Instruction Program (SI), 2001

- Geometric Number Theory (advanced topics course), Claremont McKenna College, Instructor
- Coding Theory (advanced topics course), Claremont McKenna College, Instructor
- Number Theory and Connections to Computer Science, Claremont McKenna College, Instructor
- Transcendental Number Theory (advanced topics course), Claremont McKenna College, Instructor
- Algebraic Number Theory (advanced topics course), Claremont McKenna College, Instructor
- Abstract Algebra II: Galois Theory, Claremont McKenna College, Instructor
- Abstract Algebra I, Claremont McKenna College, Instructor
- Discrete Geometry (advanced topics course), Claremont McKenna College, Instructor
- Linear Algebra, Claremont McKenna College, Instructor
- Number Theory, Claremont McKenna College, Instructor
- Calculus I, II, III, Calculus III (regular and honors), Claremont McKenna College,
Instructor

- Diophantine Approximations and Geometry of Numbers (graduate special topics course), Texas A&M University, Instructor
- Linear Algebra (Honors) for math and science majors, Texas A&M University, Instructor
- Linear Algebra for engineering majors, Texas A&M University, Instructor
- Analytic Geometry and Calculus for math and science majors, Texas A&M University, Instructor
- Engineering Calculus II (Honors), Texas A&M University, Instructor
- REU/VIGRE Course: Algebraic Methods in Computational Biology, Texas A&M University, Assistant Instructor
- Methods of Applied Mathematics I (graduate engineering
course), Texas A&M
University, Instructor

- Elementary Functions and Coordinate Geometry (Precalculus), University of Texas at Austin,
Instructor

- Differential and Integral Calculus (first and second
semesters), University of
Texas at Austin, Teaching Assistant

- Calculus for Business and Economics, University of Texas at Austin, Teaching Assistant
- Differential Equations, University of Texas at Austin, Teaching Assistant

- Geometric Number Theory: lecture notes for the special topics course at Claremont McKenna, Spring 2019
- Transcendental Number Theory: lecture notes for the special
topics course at Claremont McKenna, Spring 2015

- Discrete Geometry: lecture notes for the special topics course
at Claremont McKenna, Fall 2008 and Fall 2013

- Diophantine Approximation and Geometry of Numbers: lecture notes for the special topics course at Texas A&M, Spring 2006

- Various UNIX-type operating systems, Windows, Mac OS
- C, C++, Java, SQL, and other programming languages
- TCP/IP, CGI, ASP, and other communication protocols
- DB2, Oracle, and other database systems