Curriculum Vitae
Lenny Fukshansky
Address
Department of Mathematics
Claremont McKenna
College
850 Columbia
Avenue
Claremont, CA
91711
Phone:
(909) 607 - 0014
Fax:
(909)
621 - 8419
Email:
lenny@cmc.edu
Webpage:
http://math.cmc.edu/lenny/
Personal
- Citizenship: USA
- Born in Leningrad, Russia
- Fluent in Russian (native) and English
languages
- Member of AMS (American Mathematical
Soicety)
- Founding member of AMR (Association for
Mathematical Research)
Education
- 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
Professional Experience
- 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
Visiting Positions
- 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
Invited Research Visits
- 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
Research Interests
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
Publications
- 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 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 David Kogan) Cyclic and
well-rounded lattices, Moscow
Journal of Combinatorics and Number Theory, vol. 11 no. 1 (2022), pg. 79--96
- (with Maxwell Forst) Counting basis
extensions in a lattice, Proceedings of the American Mathematical
Society, vol. 150 no. 8 (2022), pg. 3199--3213
- (with Siki Wang) Positive semigroups in
lattices and totally real number fields, Advances
in Geometry, vol.
22 no. 4 (2022), pg. 503--512
- (with
David Kogan) On average coherence of cyclotomic
lattices, Communications in Mathematics,
vol. 31 no. 1 (2023), pg. 57--72
- (with
Maxwell Forst) On zeros of multilinear polynomials,
Journal of Number Theory, vol. 245 (2023), pg.
169--186
- (with
Alex Hsu) Covering point-sets with parallel
hyperplanes and sparse signal recovery, Discrete
and Computational Geometry, vol. 69 no. 3 (2023),
pg. 919--930
- (with
Camilla Hollanti) Euclidean lattices: theory and
applications, Communications in Mathematics, vol. 31 no. 2 (2023) pg. 251--263
- (with
Maxwell Forst) On lattice extensions, Monatshefte
fur Mathematik, vol. 203 no. 3 (2024) pg.
613--634
- (with
Maxwell Forst) On a new absolute version of
Siegel's lemma, Research in the Mathematical Sciences,
vol. 11 no. 1 (2024), Article #10, 16 pp.
- (with
Pavel Guerzhoy and Tanis Nielsen) Deep hole
lattices and isogenies of elliptic curves, Research in Number Theory,
vol. 10 no.2 (2024), Article #33, 12 pp.
Book
- (with Stephan Garcia) Geometric Number
Theory, under contract with Cambridge University
Press
Editorial
- Communications in Mathematics, an editor (2023 - present)
- Communications in Mathematics, special
issue on Euclidean lattices: theory and applications
(2023), guest editor
- 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)
Honors, Awards, Scholarships, Funding
- Institute of Mathematical Sciences Award,
Claremont Graduate University, Fall 2022
- Avery Teaching Fellow, Claremont Graduate
University, Fall 2022
- Convocation Speaker, Claremont McKenna
College, September 2018
- Simons Foundation Collaboration Grant for
Mathematicians, 2017-2024
- 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
Invited talks
- On a new version of Siegel's lemma, workshop on "Diophantine Approximation,
Dynamics and Related Topics", Yau Center for Mathematical
Sciences, Hainan, China (January 29 - February 2, 2024)
- On a new absolute version of Siegel's lemma, ILAS Special Session on "Linear Algebra,
Matrix Theory and its Applications", JMM 2024, San
Francisco, CA (January 3-6, 2024)
- A geometric construction for integer sparse
recovery,
Combinatorics Forum, UCLA
(October 26, 2023)
- Sparsity, virtually rectangular lattices and
elliptic curves,
COGENT Seminar online (June 5, 2023)
- Geometric constructions for sparse integer
signal recovery,
Probability and Statistics Seminar, USC (April 28, 2023)
- On sparse geometry of numbers, Colloquium, University of Houston (March
8, 2023)
- Covering point-sets with parallel hyperplanes
and sparse signal recovery, AMS Special Session on "Topology, Algebra
and Geometry in the Mathematics of Data Science", JMM 2023,
Boston, MA (January 4-7, 2023)
- Sparsity, virtually rectangular lattices and
elliptic curves, AMS
Special Session on "Quadratic Forms, Modular Forms and
Applications", JMM 2023, Boston, MA (January 4-7, 2023)
- Positive semigroups in lattices and totally
real number fields, AMS Special Session on "Number Theory at
Non-PhD Granting Institutions", JMM 2023, Boston, MA
(January 4-7, 2023)
- Lattices from group frames and vertex
transitive graphs, Point
Distributions Webinar (March 23, 2022)
- Geometric constructions for sparse integer
signal recovery,
Combinatorics Seminar,
UC Irvine (February 16, 2022)
- Geometric constructions for sparse integer
signal recovery, Workshop on Optimal Points
Configurations on Manifolds, Erwin
Schroedinger Institute, Vienna, Austria (January 17 - 21,
2022)
- 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
Contributed talks
- 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
Educational and expository talks
- A difference in numbers, Introduction to Faculty Talk Series,
Claremont McKenna College, October 2023
- Lecture course on Algebraic Number Theory, week-long course at the WAMS Summer School on Lattices, Diophantine
Approximation and Heights, Urgench State University,
Uzbekistan (June 6-10, 2022)
- 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
Local seminar talks
- Primitive elements in number fields and
Diophantine avoidance, Algebra / Number Theory / Combinatorics
Seminar, Claremont Colleges, February 2023
- Deep hole lattices and isogenies of elliptic
curves,
Algebra / Number Theory / Combinatorics Seminar, Claremont
Colleges, February 2023
- Orthogonality defect and coherence of
cyclotomic lattices, Algebra / Number Theory / Combinatorics
Seminar, Claremont Colleges, February 2023
- Positive semigroups in lattices and totally
real number fields, Algebra / Number Theory / Combinatorics
Seminar, Claremont Colleges, December 2022
- On discrete subgroups of Euclidean spaces, Analysis
Seminar, Claremont Colleges, December 2022
- On sparse geometry of numbers, Claremont
Mathematics Colloquium, Claremont Colleges, February 2022
- On frame coherence and nearly orthogonal
lattices,
Algebra / Number Theory / Combinatorics Seminar, Claremont
Colleges, February 2022
- 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
Other special programs and conferences attended
- 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
Research supervision and mentoring
Postdoctoral fellows
supervision
· David Krumm (at Claremont McKenna College),
2013 - 2015
· 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. from Claremont Graduate
University, August 2022
· Maxwell Forst, Ph.D. from Claremont Graduate
University, August 2023
· Sehun Jeong, Ph.D. in progress at Claremont
Graduate University
· Stephanie Reyes, 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, Ph.D.
August 2022)
· External Examiner for Aled Williams's Ph.D.
Dissertation (Cardiff University, Ph.D. February 2022)
· 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 Danzhe Chen
(Claremont McKenna College, B.A. expected May 2024)
· Advisor for senior thesis student Tanis
Nielsen (Harvey Mudd College, B.A. May 2023)
· Advisor for senior thesis student Carl Bell
(Pomona College, B.A. May 2023)
· Advisor for senior thesis student Siki Wang
(Claremont McKenna College, B.A. 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
Other mentoring activities
- Mentor for the MAA Project
NExT fellow Konrad Aguilar (Pomona College)
Professional activities and service
- Member of the scientific committee for the
CIMPA Summer School on Lattices, Diophantine Approximation
and Heights, Urgench State University, Uzbekistan (June 24
- July 5, 2024)
- Co-organizer (with D. Froncek, Z. Liu and
K. Petersen) of the Number Theory and Combinatorics in
Duluth, University of Minnesota Duluth (July 31 - August
4, 2023)
- Member of the scientific committee for the
WAMS Summer School on Lattices, Diophantine Approximation
and Heights, Urgench State University, Uzbekistan (June
6-10, 2022)
- Member of the scientific committee for the
Southern California Discrete Mathematics Symposium, 2020 -
present
- Co-organizer (with Y. Demiroglu and P.
Galashin) of the Southern California Discrete
Mathematics Symposium 2022, Claremont, California (May
1, 2022)
- 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: Diophantine Approximation
and Analytic Number Theory in Honor of Jeffrey Vaaler
at the Joint Mathematics Meeting - 2018, San Diego,
California (January 12 - 13, 2013)
- 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
- Mathematical Research Letters
- La Mathematica
- Illinois Journal of Mathematics
- TWMS Journal of Applied and Engineering
Mathematics
- SIAM Journal on Applied Algebra and
Geometry
- Lithuanian Mathematical Journal
- Journal of Knot Theory and its
Ramifications
- Semigroup Forum
- 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)
Special Teaching and Outreach Activities
- 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
Courses Taught
- Topics in Discrete Optimization (graduate
topics course), Claremont Graduate University,
Instructor
- Algebraic and Transcendental Numbers
(advanced topics course), Claremont McKenna College,
Instructor
- 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
Lecture Notes (available on the webpage in PDF format)
- Topics in Discrete Optimization: lecture
notes for the graduate topics course at Claremont Graduate
University, Fall 2022
- 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
Computing Skills
- 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