Selected Research Presentations

• From Grassmannians to Automated Geometric Proof, Colloquium, George Mason University, 19 APR 2019. PDF
• Incidence Geometry and the Area Principle, USNA Basic Notions Seminar, 26 MAR 2019. PDF
• An Invariant Version of the Power of a Point Theorem, MD/DC/VA Meeting of the MAA, Frederick Community College, 12 APR 2019. PDF
• A Binomial Proof of a Five Circle Incidence Theorem, Joint Math Meetings, Special Session in Memory of T.S. Michael, 16 JAN 2019 PDF
• Introduction to Machine Learning, USNA Basic Notions Seminar, 26 APR 2018. PDF
• Ten Points on a Cubic, MathFest, Washington, DC, 7 AUG 2015. PDF Pic
• Motivating Intersection Theory via Enumerative Geometry, James Madison University, Harrisonburg, VA, 27 APR 2015. PDF
• Geometry: Old and New, MD-DC-VA Section Meeting of the Mathematical Association of America, Roanoke College, Roanoke, VA, 25 APR 2015. PDF
• 10 points on a cubic curve, Commutative Algebra meets Alebraic Combinatorics, Queen's University, Kingston, ON, Canada, 25 JAN 2015. PDF
• Geometry: Old and New, St. Mary's College of Maryland Natural Science and Mathematics Colloquium, 21 OCT 2014. PDF
• Undergraduate Research at USNA: Making Research Projects Work for YOU, MAA MathFest, 10 AUG 2014. PDF
• The Heinz Problem, Commutative Algebra meets Algebraic Combinatorics, Dalhousie University, 24 JAN 2014. PDF
• The Enumerative Geometry of Hyperplane Arrangements, Algebraic Geometry Seminar, University of Nebraska at Lincoln, 06 DEC 2013. PDF
• From Pappus to Cayley, and Bach(arach), Basic Notions Seminar, USNA, 23 OCT 2013. PDF
• Overview of Compressed Sensing, Compressed Sensing Seminar, USNA, 17 OCT 2013. PDF
• Enumerative Geometry of Hyperplane Arrangements, CAGE Seminar, Drexel University and the University of Pennsylvania, 08 OCT 2013. PDF
• Generalizing Pascal's Theorem, Bi-College Colloquium, Haverford College and Bryn Mawr College, 07 OCT 2013. PDF
• Differential Operators and Invariant Theory, SIAM Conference on Algebraic Geometry, Colorado State University, 04 AUG 2013. PDF
• Generalizing Pascal’s Mystic Hexagon Theorem, Math Department Colloquium, Dalhousie University, RTG Workshop on Tensor Geometry, U.C. Berkeley, 18 APR 2013. PDF
• From Pascal’s Mystic Hexagon Theorem to Secant Varieties, Commutative Algebra Seminar, The University of Michigan, 14 MAR 2013.
• From Pascal’s Mystic Hexagon Theorem to Secant Varieties, RTG Workshop on Tensor Geometry, U.C. Berkeley, 28 SEPT 2012. PDF
• Counting Hyperplane Arrangements, Queen's University, 26 JULY 2012. PDF
• Families of Free Hyperplane Arrangements, Joint Mathematics Meetings, New Orleans, LA, 09 JAN 2011. PDF
• Subspace Arrangements Yearning for Freedom, AMS Section Meeting, Lexington, KY, 27 MAR 2010. PDF
• Reconstructing Hyperplane Arrangements, MD-DC-VA MAA Section Meeting, Hood College, 08 NOV 2008. PDF
• Differential Operators and Invariant Theory, Representation Theory, Systems of Differential Equations and their Related Topics Hokkaido University, Japan 5 JULY 2007. PDF
• The Fundamental Theorem of Invariant Theory, Math Department Colloquium, USNA, 15 NOV 2006. PDF
• Differential Operators on Rings of Invariants, RICAM, Linz, Austria, 15 MAY 2006. PDF
• Counting Conics, Math Department Colloquium, Howard University, Washington, D.C., 18 NOV 2005. PDF
• Counting Conics, Queen’s University Algebraic Curves Seminar, 17 OCT 2005.
• Counting Conics, Dalhousie University Mathematics Colloquium, 3 OCT 2005.
• Differential Operators and Invariant Theory, Theoretical and Practical Effectivity of Gröbner Bases, Tokyo, Japan, 25 AUG 2005. PDF
• Invariants and Differential Operators, Workshop on D-modules and Hypergeometric Functions, 14 JULY 2005. PDF
• Conics on the Cubic Surface, Mid-Atlantic Algebra Conference, George Mason University, VA, 14 NOV 2004. PDF
• The Algebra of Optimization, Math Department Colloquium, USNA, 06 NOV 2003. PDF
• Differential Operators on Toric Varieties, AMS-RMSE International Meeting, Special Session, Seville, Spain, JUN 2003.
• Higher Derivations and the Steenrod Algebra, INGO European Invariant Theory Conference, Göttingen, Germany, APR 2003. PDF, Notes
• Higher Derivations in Algebraic Geometry, Math Department Colloquium, USNA, 19 MAR 2003. PDF
• Solving Equations at the Naval Academy, Maui High Performance Computing Center, JUN 2002. PDF
• A Power Series Problem Motivated by the Localization Conjecture, AMS Section Meeting, Ann Arbor, MAR 2002.
• Parallel Computation of Gröbner Bases, AMS National Meeting, San Diego, JAN 2002
• Algebraic Curves for Fun and Profit, American University Mathematics Colloquium, NOV 2002.
• Differential Simplicity, Route 81 Conference, SUNY Albany, NOV 2002.
• The Elliptic Curve Attack on RSA Encryption, MAA Section Meeting, Blacksburg, VA, OCT 2001.
• Commutative Algebra and Network Security, Mathematics Colloquium, Towson University, 5 APR 2001. PDF
• Commutative Algebra and Network Security, Mid-Atlantic Algebra Conference, Virginia Tech., MAR 2001.
• Differential Algebras on Toric Varieties, Regional AMS Meeting, Columbia University, N.Y., Special Session on Differential Algebra, NOV 2000.
• Differential Algebras on Toric Varieties, AMS-IMS-SIAM Summer Research Conference, Mount Holyoke College, JUN 2000.
• Fair Cake Cutting After Su, Regional MAA Meeting, Bowie State University, APR 2000.
• Differential Simplicity implies Smoothness, Mid-Atlantic Algebra Conference, George Mason University, MAR 2000.
• Cliques at the Naval Academy, Regional MAA Meeting, Loyola College, NOV 1999.
• Differential Simplicity, Mid-West Algebraic Geometry Conference, University of Missouri, Columbia, OCT 1999.
• The Prime Directive, Mathematics Department Colloquium, USNA, FALL 1999.
• Differential Operators on Algebraic Varieties, Mathematical Sciences Research Institute, Berkeley, CA, Postdoctoral Seminar, DEC 1998.
• Derivations in Prime Characteristic, University of California, Berkeley, Eisenbud Seminar, DEC 1998.
• Commutative Algebra and Internet Reliability, Mathematical Sciences Research Institute, Berkeley, CA, Summer Program for Graduate Students, JUL 1998
• Differential Operators on Algebraic Varieties, University of Ottawa, MAR 1998.
• Differential Operators and Nakai’s Conjecture, U. S. Naval Academy, MAR 1998.
• A New Approach to Nakai’s Conjecture, AMS-MAA-AWM Joint Meetings, Baltimore, MD, Special Session in Commutative Algebra, JAN 1998.
• Tight Closure and Nakai’s Conjecture, Purdue University, NOV 1997.
• Nakai’s Conjecture in Prime Characteristic, Midwest Algebraic Geometry Conference, University of Notre Dame, NOV 1997.
• Nakai’s Conjecture for Curves, Route 81 Conference, Cornell University, OCT 1997.
• Higher Derivations, Queen's University, AUG 1997.
• Higher Derivations and Differential Operators, The University of Michigan, Summer Algebraic Geometry Seminar, AUG 1997.
• Differential Operators on Algebraic Varieties, Colloque des Etudiants Avances du Quebec, Universite de Montreal, MAR 1997.
• Excellent Rings and Resolution of Singularities, AMS Special Conference on Algebraic Geometry, Santa Cruz, CA, Graduate Student Session, JUL 1995.

Selected Academic Presentations

• Critical Thinking in Data Science. Lightning talk at 2019 National Workshop on Data Science Education, Bekerley, CA, 27 JUNE 2019. PDF
• Creating Course Websites with Google Sites, USNA Teaching Seminar, 08 DEC 2014. PDF
• What is Infinity?, Naval Academy Summer Seminar, 11 and 18 JUNE 2013. PDF
• Secret Sharing and Cryptography, Naval Academy Summer Seminar, 20 JUNE 2011. PDF
• Solving Systems of Polynomial Equations, Basic Notions Seminar USNA Math Dept. 08 NOV 2010. PDF
• Secret Sharing and Cryptography, Naval Academy Summer Seminar, 22 JUNE 2010.
• Game Theory, Presentation to SM280 (Topics in Mathematics), USNA, 04 NOV 2008. PDF
• Game Theory, Naval Academy Summer Seminar, 2 and 17 JUNE 2008. PDF
• Where Do Curves Go When They Meet at Infinity? Math Club, USNA, 21 SEPT 2006. PDF
• Cryptography, Presentation to SM280 (Topics in Mathematics), USNA, 19 SEPT 2006. PDF
• The Value of Money, Summer Seminar, USNA, JUN 2001.
• A Brief History of Numbers, SIMMER Invited Lecture, The Fields Institute, Toronto, MAY 1997.
• Group Cohomology (2 lectures), The Fields Institute, Toronto, FALL 1995.

Posters

• Enumerative Geometry of Hyperplane Arrangements, Workshop on Hyperplane Arrangements in the Pyrennes, Pau, France, JUNE 2012. PDF (A2 size)
• The Roller Coaster Conjecture for Artin Level Algebras, Conference on Zero-dimensional Schemes and Related Topics, Acireale, Italy (Sicily), JUNE 2002. PDF