I earned my PhD in Mathematics from Purdue University in 2007 under the direction of Professor Bernd Ulrich, and I held postdoctoral positions at
the University of Kansas and the
University of Illinois at UrbanaChampaign, and an Assistant Professor position at Cleveland State University
before joining the math department at DePaul University. My research interests are in Commutative Algebra, Algebraic Geometry and Combinatorics.
Publications

Multiplicity sequence and integral dependence, with C. Polini, N. V. Trung and B. Ulrich. To appear in Mathematische Annalen.

A Generalization of an Inequality of Lech Relating Multiplicity and Colength,
with C. Huneke and I. Smirnov, Comm. Alg. 47 (2019), 24362449.

HilbertKunz Multiplicity of the Product of Ideals,
with N. Epstein, J. Commut. Alg. 2 (2019), 225236.

Generalized Multiplicities of Edge Ideals,
with I. Soprunov and A. Alilooee, J. Alg. Comb. 47 (2018) 441472.

Uniform Symbolic Topologies and Finite Extensions,
with C. Huneke and D. Katz, J. Pure Appl. Algebra, 219 (2015) 543550.

Syzygies and Singularities of Tensor Product Surfaces of Bidegree (2,1),
with H. Schenck and A. Seceleanu, Math. Comp. 83 (2014), 13371372.

On the Equality of Ordinary and Symbolic Powers of Ideals,
with A. Hosry and Y. Kim, J. Commut. Alg. 4 (2012), 281292.

Relative Multiplicities of Graded Algebras,
J. Algebra 333 (2011), 1425.

Numerical Criteria For Integral Dependence,
with B. Ulrich, Math. Proc. Camb. Phil. Soc. 151 (2011), 95102.

Multiplicities and Rees Valuations,
with D. Katz, Collectanea Math. 61 (2010), 124.

Uniform Equivalence of Symbolic and Adic Topologies,
with C. Huneke and D. Katz, Illinois J. Math. 53 (2009), 325338.

A Criterion for Integral Dependence of Modules,
with B. Ulrich, Math. Res. Lett. 15 (2008), 149162.
Book
Teaching
 DePaul University:
Discrete Mathematics,
Graph Theory (Graduate),
Calculus for MathEd (Graduate),
Business Calculus.
 Cleveland State University:
Abstract Algebra,
Discrete Mathematics,
Geometry,
Junior Seminar,
Senior Project.
 University of Illinois:
Abstract Linear Algebra (Honors),
Applied Linear Algebra,
Calculus,
Differential Equations.
 University of Kansas:
Abstract Linear Algebra,
Applied Linear Algebra,
Calculus (Honors),
Geometry,
Statistics,
Vector Calculus,
Graduate and Undergraduate Reading Courses.
Awards and Service
 Instructor,
Actuarial Summer Academy, DePaul University, Summer 2019.
 Coorganizing the AlgebraCombinatoricsNumber Theory Seminar, DePaul University, Fall 2018Present.
 Coorganized the
Commutative Ring Theory Seminar, University of Illinois, 20122014.
 Coorganized the Midwest Algebra and Geometry Conference, University of Kentucky, June 2012.
 Coorganized the MRC Special Session on Commutative Algebra, New Orleans, January 2011.
 Referee for
Proceedings of the AMS,
Proceedings of the London Mathematical Society,
Illinois Journal of Mathematics,
Journal of Algebra,
Communications in Algebra,
Journal of Commutative Algebra,
Journal of Pure and Applied Algebra.
 AMSSimons Travel Grant, 20112013.
 Distinguished Teaching Award in Mathematics, University of Illinois at UrbanaChampaign, Spring 2014.
 Gold Medal Winner in the National Mathematics Olympiad, Iran, 1993.
Presentations
 Special Session on Commutative Algebra and Connections with Algebraic Geometry, Purdue University, April 2020.
 MSRI Graduate School on Commutative Algebra and its Interaction with Algebraic Geometry, University of Notre Dame, June 2019.
 Algebra, Combinatorics and Number Theory Seminar, DePaul University, Chicago, November 2018.
 Special Session on Multiplicities and Volumes, University of Michigan, October 2018.
 Algebra, Combinatorics and Number Theory Seminar, DePaul University, Chicago, May 2018.
 Commutative Algebra Seminar, Purdue University, April 2018.
 Special Session on Commutative Ring Theory, North Dakota State University, April 2016.
 Commutative Algebra Seminar, Georgia State University, April 2016.
 Commutative Algebra Seminar, Purdue University, April 2015.
 Algebra Seminar, Cleveland State University, April 2015.
 Combinatorics, Algebra, and Geometry Seminar, George Mason University, March 2015.
 Special Session on Closure Operations in Commutative Algebra, Georgetown University, March 2015.
 Algebra and Number Theory Seminar, University of Mississippi, October 2014.
 Multiplicities and Distinguishing Singularities, Department of Mathematics Colloquium, Cleveland State University, January 2014.
 Rees criteria and their applications, Department of Mathematics Colloquium, North Dakota State University, January 2014.
 JMM Special Session on Homological and Characteristic p Methods in Commutative Algebra, Baltimore, January 2014.
 Algebra and Combinatorics Seminar, DePaul University, Chicago, November 2013.
 Special Session on Recent Advances on Commutative Algebra, Louisville, October 2013.
 Numerical measures of singularity, Department of Mathematics Colloquium, University of Mississippi, August 2013.
 Criteria for integral dependence, Department of Mathematics Colloquium, University of Arkansas, January 2013.
 JMM Special Session on Commutative Algebra and Algebraic Geometry, San Diego, January 2013.
 Special Session on Topics in Commutative Algebra, University of Arizona, Tucson, October 2012.
 Special Session on Toric Algebraic Geometry and Beyond, University of Akron, October 2012.
 Special Session on Geometric Modeling, and Algebraic Geometry, New Orleans, October 2012.
 Special Session on Commutative Algebra, University of Akron, October 2012.
 AlgebraGeometryCombinatorics Seminar, University of Illinois, October 2012.
 Commutative Ring Theory Seminar, University of Illinois, September 2012.
 Midwest Commutative Algebra and Geometry Conference, Purdue University, May 2011.
 Commutative Algebra Seminar, UC Riverside, March 2011.
 Algebra, Geometry and Combinatorics Day, Purdue University, March 2011.
 Special Session on Geometric Modeling, and Algebraic Geometry, New Orleans, January 2011.
 MRC Workshop in Commutative Algebra, Snowbird, Utah, June 2010.
 Special Session on Commutative Algebra, University of Kentucky, March 2010.
 Department of Mathematics Colloquium, University of Missouri, February 2010.
 JMM Special Session on Commutative Algebra, San Francisco, January 2010.
 AMS Special Session on Homological Aspects of Module Theory, Florida Atlantic University, Oct 2009.
 Special Session on Commutative Algebra: Module and Ideal Theory, Baylor University, Oct 2009.
 KUMUNU, University of Nebraska, Lincoln, September 2009.
 Commutative Algebra Seminar, University of Kanas, March 2009.
 Commutative Algebra Seminar, Purdue University, March 2009.
 Special Session on Commutative Algebra, University of Illinois, March 2009.
 The 2nd Bluegrass Algebra Conference, University of Kentucky, March 2009.
 Commutative Algebra Seminar, University of Kanas, October 2008.
 Commutative Algebra Seminar, University of Kanas, September 2008.
 Commutative Algebra Seminar, Purdue University, September 2008.
 GeometryAlgebraSingularities Seminar, Northeastern University, Boston, March 2008.
 Commutative Algebra Seminar, University of Missouri, Columbia, March 2008.
 Commutative Algebra Seminar, University of Nebraska, Lincoln, October 2007.
 Special Session on Commutative Algebra and Algebraic Geometry, Davidson, March 2007.
 JMM Special Session on Commutative Algebra and and Algebraic Geometry, New Orleans, Jan 2007.
Meetings Attended
 SQuaRE on "Intersection numbers and criteria for integral dependence", AIM, June, 2019.
 Conference in Honor of Bernd Ulrich , University of Notre Dame, June 2019.
 DModules and Hodge Theory, University of Illinois at Chicago, November 2018.
 SQuaRE on "Intersection numbers and criteria for integral dependence", AIM, July, 2018.
 Algebraic Geometry and Its Broader Implications, University of Illinois at Chicago, March 2018.
 Commutative Algebra and Its Interactions with Algebraic Geometry, U Michigan, July 2016.
 Midwest Commutative Algebra Conference, University of Notre Dame, May 2016.
 Local and Global Methods in Algebraic Geometry, University of Illinois at Chicago, May 2016.
 Midwest Commutative Algebra Conference, Purdue University, August 2015.
 Algebra, Geometry and Combinatorics Day, DePaul University Chicago, October 2014.
 Algebra, Geometry and Combinatorics Day, Loyola University Chicago, November 2013.
 Commutative Algebra Meeting at CIRM, Luminy, France, July 2013.
 Algebra, Geometry and Combinatorics Day, University of Illinois, April 2012.
 Commutative Algebra and Algebraic Geometry Conference, University of Illinois, November 2011.
 Commutative Algebra Meeting at CIRM, Luminy, France, November 2010.
 Conference in Honor of Wolmer Vasconcelos, Olinda, Brazil, August 2009.
 The ShowMe Algebraic Geometry Workshop, Washington University, St. Louis, May 2009.
 The GSUUSC Commutative Algebra Seminar, Georgia State University, February 2009.
 The GSUUSC Commutative Algebra Seminar, University of South Carolina, November 2008.
 KUMUNU 9, University of Nebraska, September 2008.
 Conference in Honor of Mel Hochster, University of Michigan, July 2008.
 Conference in Honor of Luchezar Avramov, University of Nebraska, May 2008.
 Conference in Honor of Robin Hartshorne, University of Illinois, April 2008.
 KUMUNU 8, University of Nebraska, September 2007.
 Advances in Algebra and Geometry, MSRI, Berkeley, April 2007.
 Workshop on Integral Closure, Multiplier Ideals and Cores, AIM, Palo Alto, December 2006.
 UICPurdue Algebra and Geometry Workshop, Purdue University, December 2006.
 Midwest Algebra and Geometry Meeting, University of Notre Dame, October 2005.
 Conference in Honor of Phil Griffith, University of Illinois, September 2005.
 Summer School on Local Cohomology, Snowbird, Utah, June 2005.
 Arkansas Meeting on Tight Closure, University of Arkansas, April 2005.
 XVIII Brazilian Algebra Meeting, UNICAMP, Brazil, July 2004.
 Summer School on Commutative Algebra, ICTP, Trieste, Italy, May 2004.
 Midwest Algebra and Geometry Meeting, Purdue University, May 2004.
 Bluegrass Algebra Conference, University of Kentucky, March 2003.
 Commutative Algebra: Local and Birational Theory, MSRI, Berkeley, December 2002.
 Introductory Workshop in Commutative Algebra, MSRI, Berkeley, September 2002.
 Commutative Algebra Days, University of Nebraska, March 2002.
 Summer School on Algebraic Geometry, ICTP, Trieste, Italy, April 2000.
 The 5th International Meeting on Finite Fields, Augsburg, Germany, August 1999.
