Javid Validashti

I am a faculty member in the Department of Mathematical Sciences at DePaul University in Chicago. I earned my Ph.D. in Mathematics at Purdue University under the direction of Professor Bernd Ulrich. Prior to DePaul, I held positions at Cleveland State University, the University of Kansas, and the University of Illinois Urbana-Champaign. My research interests are in Commutative Algebra, Algebraic Geometry, and Combinatorics.

Education

Positions

Research

My research interests lie in commutative algebra, algebraic geometry, and combinatorics, with a focus on multiplicity theory and its applications in algebraic, geometric, and combinatorial structures. My work revolves around several key themes:

• Multiplicities, Integral Dependence and Equisingularity.
• Multiplicities, Edge Ideals and Edge Polytopes of Graphs.
• Inequalities for Multiplicities.
• Symbolic Powers of Ideals.
• Syzygies and Singularities.

The theory of multiplicities, centuries old, involves a rich interplay of ideas from various fields, including algebraic geometry, commutative algebra, convex geometry, and combinatorics. The first rigorous general algebraic treatment of multiplicities was given by Chevalley and Samuel for zero-dimensional ideals, and they soon became ubiquitous in commutative algebra. For instance, the Hilbert-Samuel multiplicity plays a prominent role in the theory of integral dependence of ideals due to the influential work of Rees. Multiplicity theory also has close ties with polyhedral geometry through Ehrhart theory. For example, the Hilbert-Samuel multiplicity of a zero-dimensional monomial ideal equals the normalized full-dimensional volume of the complement of its Newton polyhedron in the positive orthant. More recently, Achilles and Manaresi introduced the concept of j-multiplicity for ideals, and with B. Ulrich, we proposed the notion of ε-multiplicity, extending the classical Hilbert-Samuel multiplicity to arbitrary ideals and modules in a general algebraic setting. In a series of papers with various collaborators, we have proved these invariants valuable in commutative algebra, algebraic geometry, and combinatorics for their connections to the theory of integral closures, Rees valuations, equisingularity theory, and graph theory.


Over the years, I have had the privilege of working with leading experts from diverse fields. Below is a partial list of my collaborators and their respective institutions.

• Neil Epstein, George Mason University
• Craig Huneke, University of Virginia
• Daniel Katz, University of Kansas
• Steven Kleiman, MIT
• Kyle Petersen, DePaul University
• Claudia Polini, University of Notre Dame
• Alexandra Seceleanu, University of Nebraska-Lincoln
• Hal Schenck, Auburn University
• Ilya Smirnov, KTH Royal Institute of Technology
• Ivan Soprunov, Cleveland State University
• Ngo Viet Trung, Vietnam Academy of Science and Technology
• Bernd Ulrich, Purdue University

Publications

• Multiplicity Sequence and Integral Dependence.
  Mathematische Annalen,
  C. Polini, N.V. Trung, B. Ulrich, and J. Validashti, 378 (2020), 951-969.
• A Generalization of an Inequality of Lech Relating Multiplicity and Colength.
  Communications in Algebra,
  C. Huneke, I. Smirnov, and J. Validashti, 47 (2019), 2436-2449.
• Hilbert-Kunz Multiplicity of the Product of Ideals.
  Journal of Commutative Algebra,
  N. Epstein and J. Validashti, 2 (2019), 225-236.
• Generalized Multiplicities of Edge Ideals.
  Journal of Algebraic Combinatorics,
  A. Alilooee, I. Soprunov, and J. Validashti, 47 (2018) 441–472.
• Uniform Symbolic Topologies and Finite Extensions.
  Journal of Pure and Applied Algebra,
  C. Huneke, D. Katz, and J. Validashti, 219 (2015) 543–550.
• Syzygies and Singularities of Tensor Product Surfaces of Bidegree (2,1).
  Mathematics of Computation,
  H. Schenck, A. Seceleanu, and J. Validashti, 83 (2014), 1337-1372.
• On the Equality of Ordinary and Symbolic Powers of Ideals.
  Journal of Commutative Algebra,
  A. Hosry, Y. Kim, and J. Validashti, 4 (2012), 281–292.
• Relative Multiplicities of Graded Algebras.
  Journal of Algebra,
  J. Validashti, 333 (2011), 14–25.
• Numerical Criteria For Integral Dependence.
  Mathematical Proceedings of the Cambridge Philosophical Society,
  B. Ulrich and J. Validashti, 151 (2011), 95–102.
• Multiplicities and Rees Valuations.
  Collectanea Mathematica,
  D. Katz and J. Validashti, 61 (2010), 1–24.
• Uniform Equivalence of Symbolic and Adic Topologies.
  Illinois Journal of Mathematics,
  C. Huneke, D. Katz, and J. Validashti, 53 (2009), 325–338.
• A Criterion for Integral Dependence of Modules.
  Mathematical Research Letters,
  B. Ulrich and J. Validashti, 15 (2008), 149–162.

• Geometry, Mathematics Olympiad Series.
  J. Validashti. Fatemi Publishing House, Tehran,
  ISBN 964-318-329-7 (2006), 212 pages.

• Strongly Nontriangular Numbers.
  K. Petersen, J. Validashti, and C. Wayland. To appear in Mathematics Magazine.
• Refinements of Lech's Inequality for Hilbert-Samuel Multiplicity.
  H. Ananthnarayan, I. Soprunov, and J. Validashti.
• Principle of Specialization of Integral Dependence.
  S. Kleiman, B. Ulrich, and J. Validashti.
• Sharp Bounds on the Number of Lattice Points in Simplices.
  A. Rosenbaum Coelho, L. Cabral da Silva, M. Henrique Lima e Silva, M. Salimon Pinto, A. Tahzibi, and J. Validashti

Invited Presentations

• Measuring Complexity: From Singularities to Graphs.
  Department of Mathematics Colloquium.
  Georgia Southern University, Statesboro, November 2025.
• Multiplicities and Distinguishing Singularities.
  Department of Mathematics and Statistics Colloquium.
  Cleveland State University, Cleveland, January 2014.
• Rees Criteria and Their Applications.
  Department of Mathematics Colloquium.
  North Dakota State University, Fargo, January 2014.
• Algebraic Methods in Geometric Problems.
  Department of Mathematics Colloquium.
  University of Mississippi, Oxford, August 2013.
• Criteria for Integral Dependence.
  Department of Mathematical Sciences Colloquium.
  University of Arkansas, Fayetteville, January 2013.
• Multiplicities, Integral Dependence and Equisingularity.
  Mathematics and Physics Department Colloquium.
  University of Wisconsin-Parkside, March 2012.
• Multiplicities, Integral Dependence and Equisingularity.
  Department of Mathematics and Philosophy Colloquium.
  Western Illinois University, March 2012.
• A Numerical Condition for Equisingularity.
  Department of Mathematics Colloquium.
  University of Missouri, Columbia, February 2010.

• Lectures on Multiplicity Theory.
  MSRI Graduate School on Commutative Algebra and Its Interaction with Algebraic Geometry.
  Thematic Program in Commutative Algebra and Its Interaction with Algebraic Geometry.
  University of Notre Dame, Notre Dame, June 2019.
• Lech's Inequality.
  Workshop on Representation Theory, Homological Algebra, and Free Resolutions.
  Mathematical Sciences Research Institute (MSRI).
  Berkeley, Feb 2013.
• Comparing the Ordinary and Symbolic Powers of Ideals.
  Midwest Commutative Algebra and Geometry Conference.
  Purdue University, West Lafayette, May 2011.
• A Numerical Criterion for Equisingularity.
  Algebra, Geometry and Combinatorics Day.
  Department of Mathematics, Purdue University, West Lafayette, March 2011.
• Symbolic Powers of Ideals.
  Workshop in Commutative Algebra.
  Mathematics Research Communities (MRC),
  Snowbird, Utah, June 2010.
• Multiplicities, Integral Dependence and Equisingularity Theory.
  KUMUNU, Annual Conference in Commutative Algebra.
  Department of Mathematics, University of Nebraska-Lincoln, September 2009.
• Multiplicities and Integral Dependence.
  The 2nd Bluegrass Algebra Conference.
  University of Kentucky, Lexington, March 2009.

• Multiplicity Sequence and Integral Dependence.
  AMS Special Session on Commutative Algebra and Connections with Algebraic Geometry.
  Purdue University, West Lafayette, March 2022.
  
• AMS Special Session on Commutative Algebra and Connections with Algebraic Geometry.
  Purdue University, West Lafayette, April 2020.
  (Invited presentation, meeting canceled due to COVID-19 outbreak)
• A Generalization of an Inequality of Lech Relating Multiplicity and Colength.
  AMS Special Session on Multiplicities and Volumes.
  University of Michigan, Ann Arbor, October 2018.
• The j-Multiplicity of Edge Ideals.
  AMS Special Session on Commutative Ring Theory.
  North Dakota State University, Fargo, April 2016.
• Hilbert-Kunz Multiplicity of Products of Ideals.
  AMS Special Session on Closure Operations in Commutative Algebra.
  Georgetown University, Washington, March 2015.
• Multiplicity Sequence of Graded Algebras.
  AMS Special Session on Homological and Characteristic p Methods in Commutative Algebra,
  Joint Mathematics Meetings, Baltimore, January 2014.
• Inequalities for Multiplicities.
  AMS Special Session on Recent Advances in Commutative Algebra,
  Louisville, October 2013.
• Uniform Symbolic Topologies and Finite Extensions.
  AMS Special Session on Commutative Algebra and Algebraic Geometry.
  Joint Mathematics Meetings, San Diego, January 2013.
• Bigraded Minimal Free Resolutions of Tensor Product Surfaces.
  AMS Special Session on Topics in Commutative Algebra.
  University of Arizona, Tucson, October 2012.
• On Syzygies and Singularities of Tensor Product Surfaces.
  AMS Special Session on Toric Algebraic Geometry and Beyond.
  University of Akron, Akron, October 2012.
• Syzygies and Singularities of Tensor Product Surfaces of Bidegree (2,1).
  AMS Special Session on Geometric Modeling, and Algebraic Geometry.
  New Orleans, October 2012.
• On Implicitization of Tensor Product Surfaces.
  AMS Special Session on Commutative Algebra.
  University of Akron, Akron, October 2012.
• Syzygies and Singularities of Tensor Product Surfaces.
  AMS Special Session on Geometric Modeling, and Algebraic Geometry.
  New Orleans, January 2011.
• Uniform Equivalence of the Ordinary and Symbolic Powers of Ideals.
  AMS Special Session on Commutative Algebra.
  University of Kentucky, Lexington, March 2010.
• A Numerical Criterion for Equisingularity.
  Special Session on Commutative Algebra.
  Joint Mathematics Meetings, San Francisco, January 2010.
• Multiplicities and Rees Valuations.
  AMS Special Session on Homological Aspects of Module Theory.
  Florida Atlantic University, Boca Raton, Oct 2009.
• Relative Multiplicities of Graded Algebras.
  AMS Special Session on Commutative Algebra: Module and Ideal Theory.
  Baylor University, Waco, Oct 2009.
• Relative Multiplicities of Graded Algebras.
  AMS Special Session on Commutative Algebra.
  University of Illinois Urbana-Champaign, March 2009.
• A Criterion for Integral Dependence of Modules.
  AMS Special Session on Commutative Algebra and Algebraic Geometry.
  Davidson, March 2007.
• A Numerical Criterion for Integral Dependence of Modules.
  Special Session on Commutative Algebra and Algebraic Geometry.
  Joint Mathematics Meetings, New Orleans, Jan 2007.

• Loyola University, Chicago.
  Topology, Algebra, Combinatorics, and Operators Seminar, October 2025.
• University of São Paulo, São Carlos, Brazil.
  Seminar at the Institute of Mathematical and Computer Sciences (ICMC-USP), January 2025.
• Purdue University, West Lafayette.
  Commutative Algebra Seminar, September 2008, March 2009, April 2015, April 2018, March 2024.
• DePaul University, Chicago.
  Algebra, Combinatorics, and Number Theory Seminar, November 2013, May 2018, November 2018, May 2022.
• Georgia State University, Atlanta.
  Commutative Algebra Seminar, April 2016.
• Cleveland State University, Cleveland.
  Algebra Seminar, April 2015.
• George Mason University, Fairfax.
  Combinatorics, Algebra, and Geometry Seminar, March 2015.
• University of Mississippi, Oxford.
  Algebra and Number Theory Seminar, October 2014.
• University of Illinois Urbana-Champaign.
  Algebra-Geometry-Combinatorics Seminar, October 2012.
  Commutative Ring Theory Seminar, September 2012.
  
• University of California, Riverside.
  Commutative Algebra Seminar, March 2011.
• University of Kansas, Lawrence.
  Commutative Algebra Seminar, September and October 2008, March 2009.
• Northeastern University, Boston.
  Geometry-Algebra-Singularities Seminar, March 2008.
• University of Missouri, Columbia.
  Commutative Algebra Seminar, March 2008.
• University of Nebraska-Lincoln.
  Commutative Algebra Seminar, October 2007.

Research Meetings

• Equisingularity Theory and Numerical Criteria for Integral Dependence.
  Multi-year AIM SQuaRE Research Group with S. Kleiman, C. Polini, N.V. Trung, and B. Ulrich.
  California Institute of Technology, February 2025, April 2026 (Upcoming).
• Intersection Numbers and Criteria for Integral Dependence.
  Multi-year AIM SQuaRE Research Group with C. Polini, N.V. Trung and B. Ulrich.
  Palo Alto, July 2018, June 2019, June 2022.
• Workshop on Integral Closure, Multiplier Ideals and Cores.
  Palo Alto, December 2006.

• The Ubiquity of Commutative Algebra.
  Luminy, France, March 2026 (Upcoming).
• Commutative Algebra and Its Interaction with Algebraic Geometry.
  Luminy, France, July 2013.
• Commutative Algebra and Its Interaction with Algebraic Geometry.
  Luminy, France, November 2010.

• Workshop on Recent Developments in Commutative Algebra.
  Berkeley, April 2024.
• Fellowship of the Ring.
  Worldwide Commutative Algebra Virtual Seminar.
  MSRI-University of Utah, April 2020-Present.
• Workshop on Representation Theory, Homological Algebra, and Free Resolutions.
  Berkeley, Feb 2013.
• Advances in Algebra and Geometry.
  Berkeley, April 2007.
• AMS-MSRI Summer School on Local Cohomology.
  Snowbird, Utah, June 2005.
• Commutative Algebra: Local and Birational Theory.
  Berkeley, December 2002.
• Introductory Workshop in Commutative Algebra.
  Berkeley, September 2002.

• Commutative Algebra and its Connections to Geometry.
  Conference in Honor of Wolmer Vasconcelos.
  Olinda, Brazil, August 2009.
• XVIII Brazilian Algebra Meeting.
  Universidade Estadual de Campinas (UNICAMP),
  Campinas, Brazil, July 2004.
• School on Commutative Algebra and Interactions with Algebraic Geometry and Combinatorics.
  International Centre for Theoretical Physics (ICTP).
  Trieste, Italy, May 2004.
• School on Vanishing Theorems and Effective Results in Algebraic Geometry.
  International Centre for Theoretical Physics (ICTP).
  Trieste, Italy, April 2000.
• The 5th International Meeting on Finite Fields.
  University of Augsburg, Augsburg, Germany, August 1999.

• Purdue University, West Lafayette.
  Algebra Across Time, Conference in Honor of William Heinzer, April 2025.
  Midwest Commutative Algebra Conference, May 2004, May 2011, August 2015.
  UIC-Purdue Algebra and Geometry Workshop, December 2006.
• University of Arkansas, Fayetteville.
  50th University of Arkansas Spring Lecture Series, Conference, May 2025.
  Arkansas Meeting on Tight Closure, April 2005.
• University of Notre Dame, Notre Dame.
  Commutative Algebra and Its Interaction with Algebraic Geometry and Algebraic Combinatorics, August 2024.
  Commutative Algebra and Its Interaction with Algebraic Geometry and Combinatorics, June 2019.
  Midwest Commutative Algebra Conference. October 2005, May 2016.
  
• DePaul University, Chicago.
  Algebra, Geometry and Combinatorics Day, Conference, October 2014, November 2020.
  
• University of Illinois Chicago.
  D-Modules and Hodge Theory, Conference, November 2018.
  Algebraic Geometry and Its Broader Implications, Conference, March 2018.
  Local and Global Methods in Algebraic Geometry, May 2016.
• University of Michigan, Ann Arbor.
  Commutative Algebra and Its Interactions with Algebraic Geometry, July 2016.
  Conference in Honor of Mel Hochster, July 2008.
• Loyola University, Chicago.
  Algebra, Geometry and Combinatorics Day, Conference, November 2013.
  
• University of Illinois Urbana-Champaign.
  Algebra, Geometry and Combinatorics Day, Conference, April 2012.
  Commutative Algebra and Algebraic Geometry Conference, November 2011.
  Algebraic Geometry and Commutative Algebra, Conference in Honor of Robin Hartshorne, April 2008.
  Conference in Honor of Phil Griffith, September 2005.
• University of Kentucky, Lexington.
  Bluegrass Algebra Conference, March 2003, March 2009, June 2012.
• MRC Workshop in Commutative Algebra.
  Mathematics Research Communities (MRC), Snowbird, Utah, June 2010.
• Washington University, St. Louis.
  The Show-Me Algebraic Geometry Workshop, May 2009.
• Georgia State University, Atlanta.
  The GSU-USC Commutative Algebra Seminar, February 2009.
  
• University of South Carolina, Columbia.
  The GSU-USC Commutative Algebra Seminar, November 2008.
• University of Nebraska-Lincoln.
  KUMUNU, Annual Conference in Commutative Algebra, September 2007-2009.
  Commutative Algebra: Connections with Algebraic Topology and Representation Theory, May 2008.
  Commutative Algebra Days, Conference, March 2002.

Teaching

Throughout my academic journey, I have had the privilege of teaching a wide range of undergraduate and graduate courses at prominent universities, including Purdue University, the University of Kansas, the University of Illinois Urbana-Champaign, Cleveland State University, and currently at DePaul University. My teaching philosophy is anchored in the principles of critical thinking, inclusivity, and structured active learning. In recognition of my effective teaching, I was awarded the Distinguished Teaching Award in Mathematics at the University of Illinois Urbana-Champaign in 2014. Since joining DePaul University in 2018, my primary focus has been delivering high-quality lectures and ensuring accessibility in my classes. I have completed the DePaul Online Teaching Series program and have designed and offered several online courses, leveraging innovative instructional technologies to enhance student engagement and learning outcomes.

In addition to my classroom teaching, I have been involved in various service and outreach activities. For instance, I served on the Discrete Mathematics Redesign Committee at DePaul and collaborated with my colleagues to revamp the Discrete Mathematics curriculum. During the summer of 2019, I served as the lead instructor at the Actuarial Summer Academy, held at the Center for Risk Management in the Driehaus College of Business at DePaul. Furthermore, I had the privilege of delivering a series of lectures on Multiplicity Theory during the MSRI Graduate School's program on Commutative Algebra and its Interaction with Algebraic Geometry at the University of Notre Dame as part of the Thematic Program in Commutative Algebra and its Interaction with Algebraic Geometry in June 2019.

Below is a list of courses I have taught at different institutions.

• MAT140 - Discrete Mathematics I
• MAT141 - Discrete Mathematics II
• MAT135 - Business Calculus I
• MAT136 - Business Calculus II
• MAT156 - Calculus II
• MAT220 - Applied Linear Algebra
• MAT305 - Graph Theory
• MAT399 - Independent Study
• MAT494 - Graduate Graph Theory
• MAT610 - Graduate Calculus I
• MAT611 - Graduate Calculus II
• MAT612 - Graduate Calculus III
• MAT640 - Graduate Multivariable Calculus I
• CSC400 - Graduate Discrete Mathematics

• MTH 220 - Discrete Mathematics
• MTH 333 - Geometry
• MTH 358 - Abstract Algebra
• MTH 396 - Junior Seminar
• MTH 496 - Undergraduate Senior Project

• MATH 221 - Calculus I
• MATH 231 - Calculus II
• MATH 285 - Differential Equations
• MATH 415 - Applied Linear Algebra
• MATH 416 - Abstract Linear Algebra - Honors

• MATH 121 - Calculus I
• MATH 116 - Calculus II
• MATH 142 - Calculus II - Honors
• MATH 223 - Vector Calculus
• MATH 290 - Applied Linear Algebra
• MATH 365 - Statistics
• MATH 559 - Modern Geometries
• MATH 590 - Abstract Linear Algebra
• MATH 296 - Undergraduate Reading Course
• MATH 596 - Graduate Reading Course

• AI in Scientific Discovery Symposium, Participant.
  DePaul University, Chicago, May and October 2024.
  Explored applications of AI in healthcare and scientific research, with an emphasis on interdisciplinary approaches.
  
• AI in Teaching Symposium, Participant.
  DePaul University, Chicago, May and October 2024.
  Focused on integrating AI tools into teaching, including generative AI, synthetic data, and critical AI literacy.
  
• DePaul Teaching and Learning Certificate Program, Participant.
  DePaul University, Chicago, May 2024.
  Six-week program on course design, inclusive pedagogy, assessment strategies, and active learning.
  
• Cultivating Equity and Access in the Classroom, Participant.
  DePaul University, Chicago, May 2024.
  Presentation on inclusive teaching strategies and effective feedback practices.
  
• The 29th Annual Teaching and Learning Conference, Participant.
  DePaul University, Chicago, May 2024.
  
• Inclusive Teaching Through Active Learning Forum, Participant.
  DePaul University, Chicago, October 2023.
  Forum on structured active learning techniques to support equitable and effective classroom engagement.
  
• DePaul Online Teaching Series, Participant.
  DePaul University, Chicago, December 2020.
  Thirty-hour faculty development program on online course design and digital instructional methods.
  

Service

• Departmental Seminars and Colloquia, Co-organizer.
  Department of Mathematical Sciences, DePaul University, Chicago, Fall 2018–Present.
  Member, Mathematics Seminars and Colloquia Committee. Organize the Department Colloquia, Algebra–Combinatorics–Number Theory Seminar, and Joint Math/CS Seminar.
• Graduate Mathematics Education Program Committee, Member.
  Department of Mathematical Sciences,
  DePaul University, Chicago, Fall 2020–Present.
• Discrete Mathematics Redesign Committee, Member.
  Department of Mathematical Sciences, DePaul University, Chicago, Fall 2021–Present.
  Collaborate with the committee members to revamp the Discrete Mathematics curriculum and assist in developing lecture notes and online WeBWorK assignments.
• Community Building and Outreach Committee, Member.
  Department of Mathematical Sciences, DePaul University, Chicago, Fall 2025–Present.
  Organize departmental social events and contribute to the department newsletter.
• Mathematical Assessment Project, Committee Member.
  Department of Mathematical Sciences, DePaul University, Chicago, Fall 2018.
  Contributed to assessing the department’s undergraduate Learning Goals by analyzing and evaluating Learning Outcomes within the Math/CS degree program.

• Annual Undergraduate STEM Research Showcase, Reviewer.
  DePaul University, Chicago, November 2023–2025.
  Served as a reviewer at the Annual Undergraduate STEM Research Showcase, an event to provide undergraduates with a platform to present their research projects.
• Admitted Freshmen Preview Days, Faculty Presenter.
  DePaul University, Chicago, February 2024.
  Conducted 'mini classes' aimed at providing newly admitted students with an in-depth look at academic colleges, including meeting faculty and participating in sample classes.

• Student Summer Research, Co-lead.
  College of Science and Health Summer Research Institute, DePaul University, Summer 2025.
  Co-led a project guiding undergraduate students in applying calculus, mathematical modeling, and data visualization to optimize facility placement.
• Research Experience for Undergraduate Students, Mentor.
  University of São Paulo, São Carlo, Brazil, January 2025.
  Mentored a project exploring lattice points and volume relationships in polytopes
• Actuarial Summer Academy, Instructor.
  Center for Risk Management, Driehaus College of Business, DePaul University, Chicago, Summer 2019.
  Led the instruction of DePaul University's Actuarial Summer Academy, a program designed to introduce high school students to the field of actuarial science through immersive learning experiences.

• QED - Chicago's Youth Math Symposium, Judge.
  Math Circles of Chicago, Walter Payton College Prep, December 2023–2025.
  Evaluated and provided feedback to students during the symposium, offering guidance on research projects, papers, and presentations.
• Algebra, Geometry and Combinatorics Day, Co-organizer.
  DePaul University, Chicago, November 2020.
• Bluegrass Algebra Conference, Co-organizer.
  University of Kentucky, Lexington, June 2012.
• Special Session in Commutative Algebra, Co-organizer.
  Mathematics Research Communities (MRC),
  Joint Mathematics Meetings, New Orleans, January 2010.
• Instructor, Iran National Team for the International Mathematical Olympiad.
  Department of Mathematics, Sharif University of Technology, 1993-1999.
  Served as an instructor for Iran's International Mathematics Olympiad Team, sharing my experience as a former gold medal winner in the National Mathematics Olympiad in 1993. Authored a book on a problem-solving approach to geometry, a resource for students preparing for Mathematics Olympiads. The book was first published in 2006 and is now in its 4th printing.

• Undergraduate Mathematics Program Committee, Member.
  Department of Mathematics and Statistics,
  Cleveland State University, Cleveland, 2015–2017.
• Graduate Mathematics Program Committee, Member.
  Department of Mathematics and Statistics,
  Cleveland State University, Cleveland, 2015–2016.
• Instructors Evaluation Committee, Member.
  Department of Mathematics and Statistics,
  Cleveland State University, Cleveland, Fall 2016.
• Commutative Ring Theory Seminar, Co-organizer.
  Department of Mathematics,
  University of Illinois Urbana-Champaign, 2012–2014.
• Ph.D Prelim Exam, Referee.
  Department of Mathematics,
  University of Illinois Urbana-Champaign, Feb 2014.
• Mathematics Honors Program, External Examiner.
  Knox College, Galesburg, May 2012.
• Commutative Algebra Graduate Student Seminar, Co-organizer.
  Department of Mathematics,
  Purdue University, West Lafayette, Fall 2006–Spring 2007.

Reviewed manuscripts for journals, including:

• Communications in Algebra
• Illinois Journal of Mathematics
• Inventiones Mathematicae
• International Journal of Algebra and Computation
• Journal of Algebra
• Journal of Commutative Algebra
• Journal of the London Mathematical Society
• Journal of Pure and Applied Algebra
• Journal of Symbolic Computation
• Michigan Mathematical Journal
• NSA Mathematical Sciences Grants
• Proceedings of the AMS
• Proceedings of the London Mathematical Society
• Rocky Mountain Journal of Mathematics

Awards

• Recognized by DePaul Students for Support and Mentorship.
  DePaul University, Chicago, February 2025.
  Identified by students in the “Banish the Winter Blues” campus initiative as a trusted and supportive faculty member.
• Nominee, Quality of Instruction Council Excellence in Teaching Award.
  College of Science and Health, DePaul University, March 2024.
  Advanced to the final round of consideration for the Excellence in Teaching Award. Recognized for outstanding teaching effectiveness and contributions to the College of Sciences and Health.
• Distinguished Teaching Award in Mathematics.
  Mathematics Department, University of Illinois Urbana-Champaign, Spring 2014.
• AMS–Simons Travel Grant, 2011–2013.
• Competitive One-Year Postgraduate Scholarship.
  International Centre for Theoretical Physics (ICTP),
  Trieste, Italy, 1999-2000.

Mathematical Journeys

My endeavors in mathematics have taken me to wonderful places around the world! Below is a map of the locations I have visited for various mathematical events.

DePaul Math Seminars

• November 14, 2025 – Department of Mathematical Sciences Colloquium
  Laura Schaposnik (University of Illinois Chicago)
  Title: A Geometric Stroll Through Science and a Mathematician's Path
  
• October 24, 2025 – Analysis and Modeling Seminar
  Speaker: Desale Habtezghi (DePaul)
  Title: Rank U.S. States Based on Cancer-Related Attributes
  
• October 3, 2025 – Analysis and Modeling Seminar
  Speaker: Tian Jing (University of Michigan)
  Title: The Two-Phase Magnetohydrodynamic Flows: Models and Analysis
  
• September 19, 2025 – Analysis and Modeling Seminar
  Speaker: Enrico Au-Yeung (DePaul)
  Title: Rotational Symmetry and Detecting Low Emission of Radiating Sources in Nuclear Power Plants
  
• May 30, 2025 – Department of Mathematical Sciences Colloquium
  Speaker: Jimmy He (Ohio State University)
  Title: Random Growth Models with Half Space Geometry
  
• May 16, 2025 – Analysis and Modeling Seminar
  Speaker: Andrew Hicks (Carnegie Mellon)
  Title: Modeling and Numerical Analysis of the Cholesteric Landau–de Gennes model
  
• May 9, 2025 – Algebra, Combinatorics, and Number Theory Seminar
  Speaker: Jonathan Montaño (Arizona State University)
  Title: Presburger Modules: Quasi-Polynomials and Tameness
  
• May 9, 2025 – Analysis and Modeling Seminar
  Speaker: Michael Bonthron (University of Maryland)
  Title: Numerical Continuation and Applications Towards Modeling "Meta"-Materials
  
• May 2, 2025 – Analysis and Modeling Seminar
  Speaker: Williams Chukwu (DePaul)
  Title: Forecasting and Controlling Epidemics Using Mathematical Biology
  
• April 25, 2025 – Department of Mathematical Sciences Colloquium
  Speaker: Gregory G. Smith (Queen’s University)
  Title: Sums of Squares and Projective Geometry
  
• April 11, 2025 – Algebra, Combinatorics, and Number Theory Seminar
  Speaker: Claudiu Raicu (University of Notre Dame)
  Title: Polynomial Functors and Stable Cohomology
  
• March 14, 2025 – Department of Mathematical Sciences Colloquium
  Speaker: Vic Reiner (University of Minnesota)
  Title: Ehrhart Theory and a q-Analog
  
• February 7, 2025 – Department of Mathematical Sciences Colloquium
  Speaker: Sonja Petrović (Illinois Institute of Technology)
  Title: Probability and Randomness in Nonlinear Algebra 
  
• January 10, 2025 – Algebra, Combinatorics, and Number Theory Seminar
  Speaker: Maciej Piwowarczyk (University of Nebraska-Lincoln)
  Title: An Intro to (DNA) Coding Theory and Graph Constructions of Codes
  
• November 1, 2024 – Department of Mathematical Sciences Colloquium
  Speaker: Adam Gao (School of Computing - DePaul)
  Title: Learnability in Infinite-Depth Neural Networks: Overparameterization and the Role of Gaussian Processes
  
• November 8, 2024 – Joint Math-CS Seminar
  Speaker: Kyle Petersen (DePaul)
  Title: Zig-Zag Eulerian Polynomials
  
• October 11, 2024 – Analysis and Modeling Seminar
  Speaker: Jeffrey Kuan (Texas A&M University)
  Title: Universal Asymptotics through Orthogonal Polynomial Duality
  
• October 4, 2024 – Analysis and Modeling Seminar
  Speaker: Suha Jayyousi Dajani (Lake Forest College)
  Title: Multistationarity in Triple-Site Mixed Mechanism Phosphorylation Network
  
• October 4, 2024 – Algebra, Combinatorics, and Number Theory Seminar
  Speaker: Sergio Fernandez (TU-Graz)
  Title: Triangulations of Flow Polytopes and their Duals via Tropical Geometry