Javid Validashti

I am a senior lecturer in the Department of Mathematical Sciences at DePaul University in Chicago. I earned my Ph.D. in Mathematics at Purdue University in 2007 under the direction of Professor Bernd Ulrich. Prior to DePaul, I served as an Assistant Professor at Cleveland State University and held postdoctoral positions at 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, focusing 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
• Youngsu Kim, California State University, San Bernardino
• Steven Kleiman, MIT
• 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,
  with C. Polini, N.V. Trung and B. Ulrich, 378 (2020), 951-969.
• A Generalization of an Inequality of Lech Relating Multiplicity and Colength.
  Communications in Algebra,
  with C. Huneke and I. Smirnov, 47 (2019), 2436-2449.
• Hilbert-Kunz Multiplicity of the Product of Ideals.
  Journal of Commutative Algebra,
  with N. Epstein, 2 (2019), 225-236.
• Generalized Multiplicities of Edge Ideals.
  Journal of Algebraic Combinatorics,
  with I. Soprunov and A. Alilooee, 47 (2018) 441–472.
• Uniform Symbolic Topologies and Finite Extensions.
  Journal of Pure and Applied Algebra,
  with C. Huneke and D. Katz, 219 (2015) 543–550.
• Syzygies and Singularities of Tensor Product Surfaces of Bidegree (2,1).
  Mathematics of Computation,
  with H. Schenck and A. Seceleanu, 83 (2014), 1337-1372.
• On the Equality of Ordinary and Symbolic Powers of Ideals.
  Journal of Commutative Algebra,
  with A. Hosry and Y. Kim, 4 (2012), 281–292.
• Relative Multiplicities of Graded Algebras.
  Journal of Algebra,
  333 (2011), 14–25.
• Numerical Criteria For Integral Dependence.
  Mathematical Proceedings of the Cambridge Philosophical Society,
  with B. Ulrich, 151 (2011), 95–102.
• Multiplicities and Rees Valuations.
  Collectanea Mathematica,
  with D. Katz, 61 (2010), 1–24.
• Uniform Equivalence of Symbolic and Adic Topologies.
  Illinois Journal of Mathematics,
  with C. Huneke and D. Katz, 53 (2009), 325–338.
• A Criterion for Integral Dependence of Modules.
  Mathematical Research Letters,
  with B. Ulrich, 15 (2008), 149–162.

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

• Refinements of Lech's Inequality for Hilbert-Samuel Multiplicity.
  with H. Ananthnarayan and I. Soprunov.
• Principle of Specialization of Integral Dependence.
  with B. Ulrich and S. Kleiman.

Presentations

• Algebraic Multiplicities: A Combinatorial Perspective.
  Seminar at Institute of Mathematical and Computer Sciences (ICMC-USP),
  University of São Paulo, São Carlos, Brazil, January 2025.
• Combinatorial Interpretations of Multiplicities.
  Commutative Algebra Seminar,
  Department of Mathematics, Purdue University, W. Lafayette, March 2024.
• Multiplicity Sequence and Integral Dependence.
  Algebra, Combinatorics, and Number Theory Seminar,
  Department of Mathematical Sciences, DePaul University, Chicago, May 2022.
• Multiplicity Sequence and Integral Dependence.
  AMS Special Session on Commutative Algebra and Connections with Algebraic Geometry,
  Purdue University, W. Lafayette, March 2022.
  (Meeting held online due to COVID-19 outbreak)
• AMS Special Session on Commutative Algebra and Connections with Algebraic Geometry.
  Purdue University, W. Lafayette, April 2020.
  (Invited presentation, meeting canceled due to COVID-19 outbreak)
• 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.
• A Generalization of an Inequality of Lech Relating Multiplicity and Colength.
  Algebra, Combinatorics, and Number Theory Seminar,
  Department of Mathematical Sciences, DePaul University, Chicago, November 2018.
• 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.
  Algebra, Combinatorics, and Number Theory Seminar,
  Department of Mathematical Sciences, DePaul University, Chicago, May 2018.
• Generalized Multiplicities of Edge Ideals.
  Commutative Algebra Seminar,
  Department of Mathematics, Purdue University, W. Lafayette, April 2018.
• The j-Multiplicity of Edge Ideals.
  AMS Special Session on Commutative Ring Theory,
  North Dakota State University, Fargo, April 2016.
• Multiplicities of Edge Ideals.
  Commutative Algebra Seminar,
  Department of Mathematics, Georgia State University, Atlanta, April 2016.
• Multiplicity Sequences of Graded Algebras.
  Commutative Algebra Seminar,
  Department of Mathematics, Purdue University, W. Lafayette, April 2015.
• Inequalities for Multiplicities.
  Algebra Seminar,
  Department of Mathematics and Statistics, Cleveland State University, Cleveland, April 2015.
• Hilbert-Kunz Multiplicity of Products of Ideals.
  Combinatorics, Algebra, and Geometry Seminar,
  Department of Mathematics, George Mason University, Fairfax, March 2015.
• Hilbert-Kunz Multiplicity of Products of Ideals.
  AMS Special Session on Closure Operations in Commutative Algebra,
  Georgetown University, Washington, March 2015.
• Algebraic Measures of Singularity.
  Algebra and Number Theory Seminar,
  Department of Mathematics, University of Mississippi, Oxford, October 2014.
• 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.
• Multiplicity Sequence of Graded Algebras.
  AMS Special Session on Homological and Characteristic p Methods in Commutative Algebra,
  Joint Mathematics Meetings, Baltimore, January 2014.
• Multiplicities and Distinguishing Singularities.
  Algebra, Combinatorics, and Number Theory Seminar,
  Department of Mathematical Sciences, DePaul University, Chicago, November 2013.
• Inequalities for Multiplicities.
  AMS Special Session on Recent Advances in Commutative Algebra,
  Louisville, October 2013.
• Algebraic Methods in Geometric Problems.
  Department of Mathematics Colloquium,
  University of Mississippi, Oxford, August 2013.
• Lech's Inequality.
  Workshop on Representation Theory, Homological Algebra, and Free Resolutions,
  Mathematical Sciences Research Institute (MSRI),
  Berkeley, Feb 2013.
• Criteria for Integral Dependence.
  Department of Mathematical Sciences Colloquium,
  University of Arkansas, Fayetteville, January 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.
  Algebra-Geometry-Combinatorics Seminar,
  Department of Mathematics, University of Illinois Urbana-Champaign, October 2012.
• Commutative Ring Theory Seminar.
  Department of Mathematics, University of Illinois Urbana-Champaign, September 2012.
• 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.
• Comparing the Ordinary and Symbolic Powers of Ideals.
  Midwest Commutative Algebra and Geometry Conference,
  Purdue University, W. Lafayette, May 2011.
• A Numerical Criterion for Equisingularity.
  Commutative Algebra Seminar,
  Department of Mathematics, University of California Riverside, March 2011.
• A Numerical Criterion for Equisingularity.
  Algebra, Geometry and Combinatorics Day,
  Department of Mathematics, Purdue University, W. Lafayette, March 2011.
• Syzygies and Singularities of Tensor Product Surfaces.
  AMS Special Session on Geometric Modeling, and Algebraic Geometry,
  New Orleans, January 2011.
• Symbolic Powers of Ideals.
  Workshop in Commutative Algebra,
  Mathematics Research Communities (MRC),
  Snowbird, Utah, June 2010.
• Uniform Equivalence of the Ordinary and Symbolic Powers of Ideals.
  AMS Special Session on Commutative Algebra,
  University of Kentucky, Lexington, March 2010.
• A Numerical Condition for Equisingularity.
  Department of Mathematics Colloquium,
  University of Missouri, Columbia, February 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.
• Multiplicities, Integral Dependence and Equisingularity Theory.
  KUMUNU, Annual Conference in Commutative Algebra,
  Department of Mathematics, University of Nebraska, Lincoln, September 2009.
• Commutative Algebra Seminar.
  Department of Mathematics, University of Kansas, Lawrence, March 2009.
• Numerical Invariants for Integral Dependence via Epsilon Multiplicity.
  Commutative Algebra Seminar,
  Department of Mathematics, Purdue University, W. Lafayette, March 2009.
• Relative Multiplicities of Graded Algebras.
  AMS Special Session on Commutative Algebra,
  University of Illinois Urbana-Champaign, March 2009.
• Multiplicities and Integral Dependence.
  The 2nd Bluegrass Algebra Conference,
  University of Kentucky, Lexington, March 2009.
• Commutative Algebra Seminar.
  Department of Mathematics, University of Kansas, Lawrence, October 2008.
• Commutative Algebra Seminar.
  Department of Mathematics, University of Kansas, Lawrence, September 2008.
• Commutative Algebra Seminar.
  Department of Mathematics, Purdue University, W. Lafayette, September 2008.
• Geometry-Algebra-Singularities Seminar.
  Department of Mathematics, Northeastern University, Boston, March 2008.
• Commutative Algebra Seminar.
  Department of Mathematics, University of Missouri, Columbia, March 2008.
• Commutative Algebra Seminar.
  Department of Mathematics, University of Nebraska, Lincoln, October 2007.
• 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.

Meetings

• Equisingularity theory and numerical criteria for integral dependence I.
  SQuaRE Research Group with S. Kleiman, C. Polini, N.V. Trung, and B. Ulrich,
  American Institute of Mathematics (AIM),
  California Institute of Technology, February 2025.
• Commutative Algebra and its Interaction with Algebraic Geometry and Algebraic Combinatorics, Conference.
  University of Notre Dame, Notre Dame, August 2024.
• Workshop on Recent Developments in Commutative Algebra.
  The Simons Laufer Mathematical Sciences Institute (SLMath),
  Berkeley, April 2024.
• Intersection Numbers and Criteria for Integral Dependence III.
  SQuaRE Research Group with C. Polini, N.V. Trung and B. Ulrich,
  American Institute of Mathematics (AIM),
  Palo Alto, June 2022.
• Fellowship of the Ring.
  MSRI National Commutative Algebra Virtual Seminars, April 2020.
• Intersection Numbers and Criteria for Integral Dependence II.
  SQuaRE Research Group with C. Polini, N.V. Trung and B. Ulrich,
  American Institute of Mathematics (AIM),
  Palo Alto, June 2019.
• Conference in Honor of Bernd Ulrich.
  University of Notre Dame, Notre Dame, June 2019.
• D-Modules and Hodge Theory.
  University of Illinois Chicago, November 2018.
• Intersection Numbers and Criteria for Integral Dependence I.
  SQuaRE Research Group with C. Polini, N.V. Trung and B. Ulrich,
  American Institute of Mathematics (AIM),
  Palo Alto, July 2018.
• Algebraic Geometry and Its Broader Implications, Conference.
  University of Illinois Chicago, March 2018.
• Commutative Algebra and Its Interactions with Algebraic Geometry, Conference.
  University of Michigan, Ann Arbor, July 2016.
• Midwest Commutative Algebra Conference.
  University of Notre Dame, Notre Dame, May 2016.
• Local and Global Methods in Algebraic Geometry.
  University of Illinois Chicago, May 2016.
• Midwest Commutative Algebra Conference.
  Purdue University, W. Lafayette, August 2015.
• Algebra, Geometry and Combinatorics Day, Conference.
  DePaul University, Chicago, October 2014.
• Algebra, Geometry and Combinatorics Day, Conference.
  Loyola University, Chicago, November 2013.
• Commutative Algebra Research Meeting.
  Centre International de Rencontres Mathématiques (CIRM),
  Luminy, France, July 2013.
• Algebra, Geometry and Combinatorics Day, Conference.
  University of Illinois Urbana-Champaign, April 2012.
• Commutative Algebra and Algebraic Geometry Conference.
  University of Illinois Urbana-Champaign, November 2011.
• Commutative Algebra Research Meeting.
  Centre International de Rencontres Mathématiques (CIRM),
  Luminy, France, November 2010.
• Conference in Honor of Wolmer Vasconcelos.
  Olinda, Brazil, August 2009.
• The Show-Me Algebraic Geometry Workshop.
  Washington University, St. Louis, May 2009.
• The GSU-USC Commutative Algebra Seminar.
  Georgia State University, Atlanta, February 2009.
• The GSU-USC Commutative Algebra Seminar.
  University of South Carolina, Columbia, November 2008.
• KUMUNU, Annual Conference in Commutative Algebra.
  University of Nebraska, Lincoln, September 2008.
• Conference in Honor of Mel Hochster.
  University of Michigan, Ann Arbor, July 2008.
• Conference in Honor of Luchezar Avramov.
  University of Nebraska, Lincoln, May 2008.
• Conference in Honor of Robin Hartshorne.
  University of Illinois, Urbana-Champaign, April 2008.
• KUMUNU, Annual Conference in Commutative Algebra.
  University of Nebraska, Lincoln, September 2007.
• Advances in Algebra and Geometry, Conference.
  Mathematical Sciences Research Institute (MSRI),
  Berkeley, April 2007.
• Workshop on Integral Closure, Multiplier Ideals and Cores.
  American Institute of Mathematics (AIM),
  Palo Alto, December 2006.
• UIC-Purdue Algebra and Geometry Workshop.
  Purdue University, W. Lafayette, December 2006.
• Midwest Algebra and Geometry Meeting.
  University of Notre Dame, Notre Dame, October 2005.
• Conference in Honor of Phil Griffith.
  University of Illinois Urbana-Champaign,, September 2005.
• AMS-MSRI Summer School on Local Cohomology.
  Snowbird, Utah, June 2005.
• Arkansas Meeting on Tight Closure.
  University of Arkansas, Fayetteville, April 2005.
• XVIII Brazilian Algebra Meeting.
  Universidade Estadual de Campinas (UNICAMP),
  Campinas, Brazil, July 2004.
• Summer School on Commutative Algebra.
  International Centre for Theoretical Physics (ICTP),
  Trieste, Italy, May 2004.
• Midwest Algebra and Geometry Meeting.
  Purdue University, W. Lafayette, May 2004.
• Bluegrass Algebra Conference.
  University of Kentucky, Lexington, March 2003.
• Commutative Algebra: Local and Birational Theory, Conference.
  Mathematical Sciences Research Institute (MSRI),
  Berkeley, December 2002.
• Introductory Workshop in Commutative Algebra.
  Mathematical Sciences Research Institute (MSRI).
  Berkeley, September 2002.
• Commutative Algebra Days, Conference.
  University of Nebraska, Lincoln, March 2002.
• Summer School on 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.

Teaching

Throughout my academic journey, I have had the privilege of teaching a wide range of undergraduate and graduate courses at prominent universities, including Sharif University of Technology, 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. In addition, 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 - Online, In-Person
• MAT141 - Discrete Mathematics II - Online, In-Person
• MAT135 - Business Calculus I
• MAT136 - Business Calculus II
• MAT156 - Calculus II - Online, In-Person
• MAT220 - Applied Linear Algebra - Online, In-Person
• MAT305 - Graph Theory - Online, In-Person
• MAT399 - Independent Study
• MAT494 - Graduate Graph Theory - Online, In-Person
• MAT610 - Graduate Calculus I - Online, In-Person
• MAT611 - Graduate Calculus II - Online, In-Person
• MAT612 - Graduate Calculus III - Online, In-Person
• MAT640 - Graduate Multivariable Calculus I - Online, In-Person
• CSC400 - Graduate Discrete Mathematics - Online, In-Person

• 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, October 2024.
  Attended a symposium exploring the applications of Artificial Intelligence (AI) in healthcare and scientific discovery. The event featured interdisciplinary use cases, networking opportunities, and insights into AI research and collaboration across diverse fields.
  
• DePaul Teaching and Learning Certificate Program, Participant.
  DePaul University, Chicago, May 2024.
  Completed a six-week course on aligning course objectives, employing fair assessment strategies, promoting active learning, creating inclusive environments, and fostering metacognition.
  
• AI in Teaching Symposium, Participant.
  DePaul University, Chicago, October 2024.
  Attended a symposium focused on integrating AI into academic activities, with sessions on generative AI, synthetic data, AI in design, and promoting critical AI literacy.
• Cultivating Equity and Access in the Classroom, Participant.
  DePaul University, Chicago, May 2024.
  Attended a presentation on inclusive teaching strategies, including fostering student connections, promoting inclusivity, and impactful feedback.
• The 29th Annual Teaching and Learning Conference, Participant.
  DePaul University, Chicago, May 2024.
  
• AI in Teaching Symposium, Participant.
  DePaul University, Chicago, May 2024.
  Attended a symposium focused on integrating AI into academic activities, with sessions on generative AI, synthetic data, AI in design, and promoting critical AI literacy.
• Inclusive Teaching Through Active Learning Forum, Participant.
  DePaul University, Chicago, October 2023.
  Participated in a forum focused on inclusive teaching techniques, emphasizing structured active learning to create equitable classrooms and enhance student learning.
  
• DePaul Online Teaching Series, Participant.
  DePaul University, Chicago, December 2020.
  Completed a 30-hour Faculty Development Program in Online Course Design.
  

Service

• Research Experience for Undergraduate Students, Mentor.
  University of São Paulo, São Carlo, Brazil, January 2025.
  Invited to mentor a project exploring lattice points and volume relationships in polytopes.
• Department of Mathematical Sciences Colloquiums, Co-organizer.
  Department of Mathematical Sciences,
  DePaul University, Chicago, Fall 2024–Present.
• Joint Math/CS Seminar, Co-organizer.
  Department of Mathematical Sciences,
  DePaul University, Chicago, Fall 2024–Present.
• Algebra-Combinatorics-Number Theory Seminar, Co-organizer.
  Department of Mathematical Sciences,
  DePaul University, Chicago, Fall 2018–Present.
• QED - Chicago's Youth Math Symposium, Judge.
  Math Circles of Chicago, Walter Payton College Prep, December 2024.
  Evaluated and provided feedback to students during the symposium, offering guidance on research projects, papers, and presentations.
• Annual Undergraduate STEM Research Showcase, Reviewer.
  DePaul University, Chicago, November 2024.
  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, Lecturer.
  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.
• 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.
  Collaborated with the committee members to revamp the Discrete Mathematics curriculum and assisted in creating lecture notes and online WeBWorK assignments.
• QED - Chicago's Youth Math Symposium, Judge.
  Math Circles of Chicago, Walter Payton College Prep, December 2023.
  Evaluated and provided feedback to students during the symposium, offering guidance on research projects, papers, and presentations.
• Annual Undergraduate STEM Research Showcase, Reviewer.
  DePaul University, Chicago, November 2023.
  Served as a reviewer at the Annual Undergraduate STEM Research Showcase, an event to provide undergraduates with a platform to present their research projects.
• Algebra, Geometry and Combinatorics Day - Virtual Conference, Co-organizer.
  Department of Mathematical Sciences,
  DePaul University, Chicago, November 2020.
• 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.
  
• Annual Undergraduate STEM Research Showcase, Reviewer.
  DePaul University, Chicago, November 2018.
  Served as a reviewer at the Annual Undergraduate STEM Research Showcase, an event to provide undergraduates with a platform to present their research projects.
• 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.
• 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.
• Midwest Algebra and Geometry Conference, Co-organizer.
  Mathematics Department,
  University of Kentucky, Lexington, June 2012.
• Mathematics Honors Program, External Examiner.
  Knox College, Galesburg, May 2012.
• Special Session in Commutative Algebra, Co-organizer.
  Mathematics Research Communities (MRC),
  Joint Mathematics Meetings, New Orleans, January 2010.
• Commutative Algebra Graduate Student Seminar, Co-organizer.
  Department of Mathematics,
  Purdue University, W. Lafayette, Fall 2006–Spring 2007.
• Instructor, Iran’s International Mathematics Olympiad Team.
  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.

• 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

• 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.
• Postgraduate Scholarship.
  International Centre for Theoretical Physics (ICTP),
  Trieste, Italy, 1999-2000.
• Outstanding Graduate Teaching Assistant Award in Mathematics.
  Sharif University, Tehran, March 1998.
• Gold Medal, National Mathematics Olympiad.
  Iran, February 1993.

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.