Mee Seong Im

National Research Council Research Associate

National Academy of Sciences (NAS)


Army Research Laboratory

Supercomputing Research Center, Office: C-236

Aberdeen Proving Ground, MD 21005


NAS Assistant Professor

Department of Mathematical Sciences

United States Military Academy

West Point, NY 10996


Office: 252 Thayer Hall

Phone: (845) 938-5649

Fax: (845) 938-2409

Email: meeseongim *at* gmail *dot* com

Background

  • Doctor of Philosophy (Ph.D.) in Mathematics at the University of Illinois at Urbana-Champaign
  • Master of Arts (M.A.) in Mathematics at the University of Georgia
  • Master of Philosophy (M.Phil.) in Mathematics at the University of Birmingham, England
  • Bachelor of Science (B.S.) in Physics at the University of Georgia
  • Bachelor of Science (B.S.) in Mathematics at the University of Georgia

I am a National Academy of Sciences Research Associate from July 3, 2017 to July 2, 2020. I am teaching at West Point in the fall and researching with the Army Research Laboratory at Aberdeen Proving Ground, MD in the spring and in the summer.

In Fall of 2018, I am teaching

Co-organizer: I am co-organizing FPSAC 2019 (Free and Practical Software for Algebraic Combinatorics), which will take place at the University of Ljubljana in Ljubljana, Slovenia on July 8-12, 2019.

Mathematicians in all areas of mathematics and all users of sage (python), Macaulay2, Mathematica, GAP (computational discrete algebra system), Magma (computer algebra system), etc. are welcome!

Research co-leader: I am a small group research co-leader for Women in Noncommutative Algebra and Representation Theory Workshop (WINART2), which will take place at the University of Leeds, England on May 20-24, 2019.

Reviewer: I am a reviewer for Zentralblatt MATH (reviewer ID: 17038).

Managing editor: I have been on the editorial board with other Association for Women in Mathematics (AWM) mathematicians, creating Advances in the Mathematical Sciences Springer book. Hard copies may be purchased at the 2019 Joint Mathematics Meeting (January 16-19, 2019) in Baltimore, MD.

Research Interests

  • Diagrammatic algebras and categorification. quiver Hecke algebras, modified Hecke algebras, quantum group, variations of Brauer algebras, Temperley-Lieb algebras.
  • Geometric constructions. Geometric techniques, fiber bundles, Hilbert schemes and moduli spaces.
  • Equivariant geometry of algebraic groups, Lie (super)algebras, (Grothendieck-)Springer resolutions, quiver varieties, quiver flag varieties.

Keywords: geometric, categorical, combinatorial representation theory, and quantum topology.

Doctoral Dissertation

Main results include the study of semi-invariants appearing in generalized Grothendieck-Springer resolutions; their connections to filtered quiver representations are given in my dissertation, which was written under Tom Nevins' supervision.

Publications, arXiv

  • On the Hamiltonian reduction of generalized Grothendieck-Springer resolutions, with R. Lewis. In progress.
  • On quantum shuffle algebras and the characters of KLR-algebras. In progress.
  • TBA, with M. Zakrzewski, in progress, 2018.
  • Quantum computing in quantum programmable channels, with V. Dasari, in progress, 2018.
  • Quantum automata and colored HOMFLY-PT invariants (tentative title), with A. Nelson, in progress, 2018.
  • Categorification of Verma modules and indecomposable projective modules in the category I_g(sl(2)) for sl(2) II, with B. Cox, in preparation, 2018.
  • On the module structure of the center of hyperelliptic Krichever-Novikov algebras II, with B. Cox, X. Guo, K. Zhao, in preparation, 2018.
  • On cohomological properties of quiver flag varieties (tentative title), in progress, 2018.
  • Invariants of certain Lie superalgebras on super-representations on the k-Jordan quiver (tentative title), in progress, 2018.
  • On certain Lie superalgebras (tentative title), with C. Lai, A. Wilbert, J. Zhu, in progress, 2018.
  • TBA, with T. Scrimshaw, in progress, 2018.
  • TBA, with Z. Daugherty, I. Halacheva, G. Letzter, E. Norton, in progress, 2018.
  • TBA, with O. Omari, S. Reif, M. Rosas and M. Schaps, in preparation, 2018.
  • Optimization techniques in adaptive computing systems, with V. Dasari and L. Beshaj, submitted, 2018.
  • Beta super-functions on super-Grassmannians, with M. Zakrzewski, submitted, J. Math. Phys. (2018), 18 pages.
  • Categorification of Verma modules and indecomposable projective modules in the category I_g(sl(2)) for sl(2), with B. Cox, submitted, Adv. Math. (2018), 23 pages.
  • Complexity and mission computability of adaptive computing systems, with V. Dasari and B. Geerhart, submitted, J. Defense Modeling & Simulation (2018), 6 pages.
  • Optimization and synchronization of programmable quantum communication channels, with V. Dasari, Proc. SPIE Quantum Information Science, Sensing, and Computation X 10660-26 (2018), 1-7.
  • The affine VW supercategory, with M. Balagovic, Z. Daugherty, I. Entova, I. Halacheva, J. Hennig, G. Letzter, E. Norton, V. Serganova and C. Stroppel, submitted, Math. Z. (2018), 35 pages.
  • On the module structure of the center of hyperelliptic Krichever-Novikov algebras, with B. Cox, Representations of Lie Algebras, Quantum Groups and Related Topics, Contemp. Math. 713 (2018), 61-94.
  • Translation functors and decomposition numbers for the periplectic Lie superalgebra p(n), with M. Balagovic, Z. Daugherty, I. Entova, I. Halacheva, J. Hennig, G. Letzter, E. Norton, V. Serganova and C. Stroppel, accepted, Math. Res. Lett. (2016), 42 pages.
  • Unipotent invariants of filtered representations of quivers and the isospectral Hilbert scheme, with L. Jones, arXiv: 1608.02293, 2016.
  • Families of orthogonal Laurent polynomials, hyperelliptic Lie algebras and elliptic integrals, with B. Cox, Integral Transforms Spec. Funct. 27 (2016), no. 11, 899-919.
  • Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence, with A. Wu, Adv. Math. Sci. 15 (2018), 18 pages.
  • Generalized iterated wreath products of cyclic groups and rooted trees correspondence, with A. Wu, Adv. Math. Sci. 15 (2018), 15 pages.
  • On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution, IDEALS 2142 (2014), no. 49392, 1-134.
  • Suggestions to study affine and GIT quotients of the extended Grothendieck-Springer resolution, Preprint, 2014.
  • Semi-invariants of filtered quiver representations with at most two pathways, arXiv: 1409.0702, submitted, 2014.
  • The regularity of the cotangent bundle of the Grothendieck-Springer resolution, Article, 2013.
  • The regular semisimple locus of the affine quotient of the cotangent bundle of the Grothendieck-Springer resolution, J. Geom. Phys. 132 (2018), 84-98.
  • On Kostant's theorem for Lie algebra cohomology, with B. D. Boe, L. Chastkofsky, D. K. Nakano, J. R. Kujawa, E. Wiesner, I. Bagci, B. Connell, B. J. Cooper, M. S. Im, W. Li, K. J. Platt, C. B. Wright, B. Wyser and T. Kelly, Contemp. Math. 478 (2009), 39-60.
  • Nonstandard approach to Hausdorff measure theory and an analysis of some sets of dimension less than 1, eTheses Repository 5218 (2005), 1-103.
  • Examples relating to Green's conjecture in low characteristics and genera, with T. Estu, J. Manning, Z. Michaels, J. Pasko, W. Rulla and N. Wijesinghe, accepted upon revision, Experiment. Math. (2004), 17 pages.

Selected presentation slides.

  • July 2018, ICERM, Brown University, Providence, RI. [slides]
  • June 2018, Colorado State University Mountain Campus, Bellvue, CO. [slides]
  • June 2018, University of Georgia, Athens, GA. [slides]
  • May 2018, Jan Kochanowski University, Kielce, Poland. [slides]
  • Apr 2018, SPIE Defense and Security 2018, Orlando, FL. [slides, slides]
  • Apr 2018, University of Oklahoma, Norman, OK. [slides]
  • Mar 2018, Ohio State University, Columbus, OH. [slides]
  • Dec 2017, Department of Mathematics, Virginia Tech, Blacksburg, VA. [slides]
  • Oct 2017, 25th ARL-USMA Technical Symposium, Aberdeen Proving Ground, MD. [poster]
  • Jul 2017, College of Science and Technology, Temple University, Philadelphia, PA. [slides]
  • Jul 2017, Lev Campus of the Jerusalem College of Technology, Jerusalem, Israel. [slides]
  • Jul 2017, Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel. [slides]
  • May 2017, University of Reims Champagne-Ardenne, Moulin de la Housse, Reims, France. [poster]
  • Apr 2017, University of California, Los Angeles, Los Angeles, CA. [slides]
  • Apr 2017, Oklahoma State University, Stillwater, OK. [slides]
  • Jan 2017, Joint Mathematics Meeting (Lie supersubalgebras), Atlanta, GA. [slides]
  • Jan 2017, Joint Mathematics Meeting (geometry), Atlanta, GA. [slides]
  • Mar 2016, AMS Sectional Meeting, Athens, GA. [slides]
  • Jan 2016, Joint Mathematics Meeting, Seattle, WA. [slides]
  • Oct 2015, Army Research Lab, Aberdeen Proving Ground, MD. [slides]
  • May 2015, Pomona College, Claremont, CA. [slides]
  • Apr 2015, Florida Gulf Coast University, Fort Myers, FL. [slides]
  • Apr 2015, University of Maryland, College Park, MD. [poster]
  • Jan 2015, Joint Mathematics Meeting, San Antonio, TX. [slides]
  • May 2014, Alexandria, VA. [slides]
  • Apr 2014, University of California, Berkeley, CA. [slides]
  • Apr 2014, Doctoral defense, University of Illinois, Urbana, IL. [slides]
  • Apr 2014, University of Texas, Austin, TX.
  • Dec 2013, MIT Lincoln Laboratory, Lexington, MA. [slides]

Fellowships, Awards, and Grants

United States Military Academy.

  • AMS-Simons Travel Grant, July 2018 - June 2020.
    • Principal Investigator: on the diagrammatical, categorical, and combinatorical representations of periplectic Lie superalgebras.
  • Mathematical Sciences Research Institute Research Proposal, Spring 2018.
    • Principal Investigator: representation theory of superalgebras.
  • Faculty Research Fund, Spring 2018.
    • Co-Principal Investigator: on the combinatorial aspects of the representation theory of periplectic Lie superalgebras.
  • NSF-AWM Travel Grant, 2017.
    • Principal Investigator: categorification of modified KLR-algebras for the spin setting.
  • National Academy of Sciences Research Associateship, 2017.
    • Principal Investigator: quantum programmable computers.
  • National Academy of Sciences Travel Award, 2017.
    • Principal Investigator: quantum programmable computers.
  • Army Research Laboratory (ARL-USMA) Research Grant, Spring 2017.
    • Principal Investigator: quantum topology and categorical representation theory.
  • ADVANCE travel funding, Spring 2016, Spring 2017.
  • Computational Engineering Mathematics Fund, 2016-2017.
    • Principal Investigator: on the representation theory and geometric properties of Lie superalgebras and the (quantum) Hamiltonian reduction for parabolic subalgebras.
  • Faculty Research Fund, Fall 2016.
    • Principal Investigator: noncommutative algebras and algebraic geometry in sage.
  • Mathematical Sciences Center of Excellence (Applications in Computational Engineering Mathematics), 2015-2016.
    • Principal Investigator: computational mathematics in studying the fibers of generalized Springer resolutions, Khovanov homology, (rational) Cherednik algebras, and the Hilbert scheme.
  • Army Research Laboratory (ARL-USMA) Research Grant, 2015-2016.
    • Principal Investigator: computational aspects of quantum entanglement.
  • Academic Research Council: Faculty Development Research Fund (Grant), 2015-2016.
    • Principal Investigator: categorification and quantum Hamiltonian reduction of Grothendieck-Springer resolutions.

University of Illinois at Urbana-Champaign.

  • NSF-AWM Travel Grant, 2015. Full amount awarded but declined: June 3, 2015, page 15.
    • Area: noncommutative algebras and geometric & topological aspects of representation theory.
  • NSF-AWM Mentoring Grant, 2015.
    • Area: categorical representation theory.
  • AMS-MRC-NSF Collaboration Grant, 2014-2015.
    • Area: applications of representation theory.
  • Campus Research Board Research Assistantship, Summer 2013, Fall 2013, Spring 2014.
  • NSA Research Assistantship, Fall 2012, Spring 2013, Summer 2013.
  • B.G. Trijtzinsky Fellowship, Spring 2012.
  • E.T. Parker Fellowship, Spring 2011.
  • University Fellowship, Spring 2011, Spring 2012.
  • NSF REGS2 Research Fellowship, Summer 2012, Spring 2013.
  • NSF REGS Research Fellowship, Summer 2009, Summer 2010, Summer 2011.
  • Conference Travel Award, Summer 2008, Spring 2009, Fall 2010, Spring 2011, Summer 2011, Spring 2013, Spring 2014, Summer 2014, Fall 2014, Spring 2015, Summer 2015.
  • List of Teachers Ranked as Excellent, Fall 2007, Fall 2008, Spring 2009, Fall 2009, Spring 2011.
  • Teacher Scholar Certificate, April 2010.
  • Graduate Teaching Certificate, April 2010.

University of Georgia.

  • Summer Research Award, with the Department of Physics.
  • REU Summer Research Award, with the Department of Mathematics.
  • VIGRE Summer Research Award, with the Department of Mathematics.
  • Hope Scholarship, every semester.
  • Pell Grant, every semester.
  • Dean's List.

Invited Talks and Professional Training

  • TBA, Algebraic geometry seminar, TBA, Columbia University, NY.
  • October 2018, Combinatorial and Categorical Aspects of Representation Theory, Representations of degenerate affine Brauer superalgebras, San Francisco State University, San Francisco, CA. [abstract]
  • October 2018, 26th Annual ARL/USMA Research Symposium, TBA, Mallette Training Facility, APG, MD.
  • July 2018, National Academy of Sciences and Army Research Lab, On quantum programmable computers, quantum computation, and optimization problems in mission computability, Department of Mathematical Sciences, West Point, NY.
  • July 2018, Combinatorics and Representation Theory, Research and code presentation, ICERM, Brown University, Providence, RI.
  • July 2018, Combinatorics and Representation Theory, A construction of the affine VW supercategory, ICERM, Brown University, Providence, RI.
  • June 2018, The 13th Brauer group Conference, An investigation towards higher Schur-Weyl duality for the periplectic Lie superalgebra, Colorado State University Mountain Campus, Bellvue, CO.
  • June 2018, Southeastern Lie Theory Workshop X, On the affine VW supercategory, University of Georgia, Athens, GA.
  • June 2018, Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification, On the affine VW supercategory, Catholic University of America, Washington, DC.
  • May 2018, Algebra seminar, On the representation theory of periplectic Lie superalgebras and affine VW supercategory, Department of Mathematics, Jan Kochanowski University, Kielce, Poland.
  • April 2018, SPIE Defense and Security, Synchronization of programmable quantum and classical communication channels, Gaylord Palms Resort & Convention Center, Orlando, FL. [abstract]
  • April 2018, Texas-Oklahoma Representations and Automorphic Forms IX, On the affine VW supercategory, University of Oklahoma, Norman, OK.
  • March 2018, AMS Special Session: Noncommutative Algebra and Noncommutative Algebraic Geometry, On a construction of the affine VW supercategory, Ohio State University, Columbus, OH. [abstract]
  • December 2017, Algebra seminar, On higher cohomology vanishing for quiver flag varieties, Department of Mathematics, Virginia Tech, Blacksburg, VA. [abstract]
  • October 2017, 25th Annual ARL/USMA Research Symposium, A 1-categorification of Verma modules for sl(2), Mallette Training Facility, APG, MD. [abstract]
  • August 2017, National Academy of Sciences and Army Research Lab, Research Overview, Department of Mathematical Sciences, West Point, NY.
  • July 2017, Algebra Extravaganza, Cohomological properties of certain quiver flag varieties, Temple University, Philadelphia, PA. [abstract]
  • July 2017, Algebra Extravaganza, On the category of finite-dimensional representations of periplectic Lie superalgebras, Temple University, Philadelphia, PA.
  • July 2017, ACA 2017, The category of finite-dimensional representations of periplectic Lie superalgebras, Jerusalem College of Technology, Jerusalem, Israel. [abstract]
  • July 2017, Algebra seminar, On the finite-dimensional periplectic Lie superalgebra representations, Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.
  • July 2017, Algebraic Modes of Representations, The category of finite-dimensional representations of strange Lie superalgebras, Faculty of Mathematics & Computer Science, Weizmann Institute of Science, Rehovot, Israel.
  • June 2017, Summer Leaders Experience mathematics workshop, Compatibility using vectors and matrices, Department of Mathematical Sciences, West Point, NY.
  • May 2017, Representation Theory at the Crossroads of Modern Mathematics, The category of finite-dimensional integrable representations of the periplectic Lie superalgebra, Moulin de la Housse, Reims, France.
  • April 2017, Representation theory seminar, On the representation theory of periplectic Lie superalgebras, University of Massachusetts, Amherst, MA. [abstract]
  • April 2017, Sonia Kovalevsky Day, Challenge problems, luncheon workshop instructor, United States Military Academy, West Point, NY.
  • April 2017, Sonia Kovalevsky Day, Diagram algebras, United States Military Academy, West Point, NY.
  • April 2017, AWM Research Symposium, WINART: Representations of Algebras, Representations of signed affine Brauer algebras, UCLA, Los Angeles, CA. [abstract]
  • April 2017, AWM Research Symposium, Constructing symplectic varieties using geometric invariant theory, joint with N. Jimenez, UCLA, Los Angeles, CA.
  • April 2017, Texas-Oklahoma Representations and Automorphic forms VIII, Representations of affine Nazarov-Wenzl algebras, Oklahoma State University, Stillwater, OK. [abstract]
  • January 2017, JMM: Representations and Related Geometry in Lie Theory, On the geometry of filtered representations of quivers and connections to isospectral Hilbert schemes, Hyatt Regency, Atlanta, GA. [abstract]
  • January 2017, JMM: New Developments in Noncommutative Algebra and Representation Theory, Higher Schur-Weyl duality for Lie supersubalgebras, Hyatt Regency, Atlanta, GA. [abstract]
  • December 2016, Raider-Black Knight STEM Seminar, Drones and Route Planning: flight planning and flying drones, United States Military Academy, West Point, NY.
  • December 2016, Raider-Black Knight STEM Seminar, Drones and Route Planning: flight planning and flying drones, United States Military Academy, West Point, NY.
  • December 2016, Raider-Black Knight STEM Seminar, Drones and Route Planning: flight planning and flying drones, United States Military Academy, West Point, NY.
  • November 2016, Combinatorics, Symbolic Dynamics, Research and code presentation, Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel.
  • November 2016, Combinatorics, Symbolic Dynamics, Quiver Hecke algebras and related geometric constructions, Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel.
  • October 2016, Workshop on Symplectic Varieties and Geometric Representation Theory, Connecting Grothendieck-Springer resolutions to the isospectral Hilbert scheme via universal quiver flags, UNC, Chapel Hill, NC. [abstract]
  • October 2016, 24th Annual ARL/USMA Research Symposium, Towards programmable quantum networks, Mallette Training Facility, APG, MD. [abstract]
  • October 2016, 24th Annual ARL/USMA Research Symposium, Connections between the geometry of Grothendieck-Springer resolutions and the isospectral Hilbert scheme, APG, MD. [abstract]
  • September 2016, Colloquium, Quiver-graded Grothendieck-Springer resolutions and the isospectral Hilbert scheme, City College of New York, New York, NY. [abstract]
  • August 2016, International Conference on Representations of Algebras, An approach to a categorification of infinite dimensional modules for sl(2), Syracuse University, Syracuse, NY.
  • May 2016, Algebraic Groups, Quantum Groups and Geometry, Towards a categorification of infinite-dimensional modules, University of Virginia, Charlottesville, VA.
  • April 2016, Topology and Algebra Research Symposium, Techniques toward a categorification of sl(2)-Verma modules. Sam Houston State University, Huntsville, TX. [abstract]
  • March 2016, Categorical representation theory and geometrization of quiver Hecke algebras toward constructing higher categorical structure for Verma modules. Department of Physics, University of Georgia, Athens, GA. [abstract]
  • March 2016, AMS Special Session: Algebraic Structures in Mathematical Physics: Lie Algebras, Vertex Algebras, Quantum Algebras, A categorification of sl(2)-Verma modules. University of Georgia, Athens, GA. [abstract]
  • January 2016, Joint Mathematics Meeting: AMS Session on Algebraic Geometry, On the categorification of Verma modules for sl(2). Seattle, WA. [abstract]
  • October 2015, 23rd Annual ARL/USMA Research Symposium, On families of orthogonal Laurent polynomials, hyperelliptic Lie algebras and elliptic integrals, Mallette Training Facility, Aberdeen Proving Ground, MD. [abstract]
  • September 2015, Colloquium, The multidimensional aspects of quiver-graded Grothendieck-Springer resolutions, College of Charleston, Charleston, SC. [abstract]
  • July 2015, Faculty Development Workshop, Department of Mathematical Sciences, United States Military Academy, West Point, NY.
  • July 2015, Faculty Development Workshop, Department of Mathematical Sciences, United States Military Academy, West Point, NY.
  • June 2015, Algebra and Number Theory Seminar, Connecting invariants associated to generalized Grothendieck-Springer resolutions to homotopy theory. University of California, Santa Cruz, CA. [abstract]
  • May 2015, Colloquium, From a quantum field theory to categorical representation theory. Pomona College, Claremont, CA.
  • April 2015, The geometric construction of KLR-algebras. Florida Gulf Coast University, Fort Myers, FL. [abstract]
  • April 2015, On quiver Hecke, quantum shuffle, and quantum cluster characters. University of Maryland, College Park, MD. [abstract]
  • March 2015, Algebraic Combinatorics, Coding Sprints, Research and code presentation, University of California, Davis, CA.
  • March 2015, Generalizing almost-commuting varieties to Grothendieck-Springer resolutions associated to quivers: history, results, current development. Fordham University, Bronx and Manhattan, NY.
  • February 2015, Departmental talk to the faculty. United States Military Academy, West Point, NY.
  • January 2015, Joint Mathematics Meeting, Quiver Hecke algebras and filtered quiver representations. San Antonio, TX.
  • July 2014, Modern applications of representation theory, Filtered quiver representations, research presentation. University of Chicago, Chicago, IL.
  • June 2014, Representation theory in data analysis, group presentation. Mathematics Research Communities, American Mathematical Society, Salt Lake City, UT.
  • May 2014, On constructing invariants for generalized quiver varieties with applications to shape deformation in target and activity recognition. Arlington and Alexandria, VA. [abstract]
  • May 2014, Algecom-10: Algebra, Geometry, and Combinatorics Day, Viewing deformation of objects as equivalence classes of orbits on representation spaces and generalized quiver varieties, University of Illinois, Urbana, IL.
  • April 2014, Topology & Algebra Research Symposium, On filtered representations of quivers with at most two pathways and on the generalized Grothendieck-Springer resolution. University of California, Berkeley, CA.
  • April 2014, Topology and Geometry Conference, Parabolic equivariant geometry in representation theory. University of Texas, Austin, TX.
  • December 2013, Massachusetts Institute of Technology Lincoln Laboratory, Applications of filtered quiver varieties in representation theory. Lexington, MA.
  • November 2013, Colloquium, The geometry of filtered quiver varieties. Mathematics Seminar, Baltimore, MD.
  • April 2013, Graduate Research Conference in Algebra and Representation Theory, Declined, schedule conflict. Kansas State University, Manhattan, KS.
  • January 2013, Noncommutative Algebraic Geometry and Representation Theory, Invariants and semi-invariants of arbitrary filtered quiver varieties, poster presentation. MSRI, Berkeley, CA.
  • April 2011, Topology and Algebra Research Symposium, Matrix varieties: an analogue of the isospectral Hilbert scheme. University of Iowa, Iowa City, IA.
  • October 2010, Midwest Algebraic Geometry Graduate Conference, An analogue of the Hilbert scheme of n points on a complex plane. University of Wisconsin, Madison, WI.
  • September 2008, Fano manifolds and Lagrangian fibration of symplectic manifolds, An introduction to algebraic surfaces. University of Warsaw, Lukecin, Poland.
  • July 2008, Summer Program: Geometrical Singularities and Singular Geometries, Singularities in Calabi-Yau varieties. IMA, University of Minnesota, Minneapolis, MN.

United States Military Academy.

  • Spring 2017, Theoretical Mathematics seminar, Hecke algebras and perverse sheaves (postponed).
  • March 2017, Working seminar on D-modules: rings of differential operators and the Jacobian Conjecture III.
  • March 2017, Working seminar on D-modules: rings of differential operators and the Jacobian Conjecture II.
  • February 2017, Working seminar on D-modules: the Jacobian Conjecture.
  • February 2017, Working seminar on D-modules: properties of rings of differential operators.
  • February 2017, Working seminar on D-modules: rings of differential operators.
  • February 2017, Working seminar on D-modules: ideal structure of the Weyl algebra.
  • January 2017, Working seminar on D-modules. ideal structure of the Weyl algebra.
  • January 2017, Working seminar on D-modules: on properties of Weyl algebras.
  • January 2017, Theoretical Mathematics seminar, Signed string diagrammatic algebras: an introduction to signed VW-algebras. [abstract]
  • January 2017, Theoretical Mathematics seminar, On the geometry of quiver Hecke algebras. [abstract]
  • August 2016, Theoretical Mathematics seminar, The scheme of filtered representations of quivers and geometric relations to the isospectral Hilbert scheme. [abstract]
  • April 2016, Theoretical Mathematics seminar, Towards a categorification of infinite-dimensional modules. [abstract]
  • April 2016, Theoretical Mathematics seminar, Constructing an algebra isomorphism between certain Brauer algebras and the endomorphism algebra of a module.
  • December 2015, Theoretical Mathematics seminar, A (geometric) categorification of Verma modules for U(sl(2)). [abstract]
  • September 2015, Theoretical Mathematics seminar, On the multifaceted geometric aspects of Grothendieck-Springer resolutions.

University of Illinois at Urbana-Champaign.

  • May 2014, Graduate student algebraic geometry, Kazhdan-Lusztig polynomials, quiver Hecke algebras, and categorification. [abstract]
  • April 2014, Dissertation defense, On semi-invariants of filtered representations of quivers and the cotangent bundle of the Grothendieck-Springer resolution.
  • October 2013, AWM-Illinois, The evolution of invariant theory: from classics to modern.
  • October 2013, Graduate student algebraic geometry, The geometry of filtered quiver varieties.
  • December 2012, Algebraic geometry, Invariants and semi-invariants of filtered quiver representations.
  • November 2012, Pi Mu Epsilon: Illinois Honors Society, Quotients of curves and surfaces and higher dimensional analogues.
  • November 2012, AWM-Illinois, Moduli problems through representations of quivers.
  • January 2012, Graduate geometry & topology, The Hamiltonian reduction of a certain affine variety.
  • December 2011, AWM-Illinois, Geometric invariant theory.
  • March 2011, Graduate geometry & topology, On a certain family of matrices in the context of algebraic geometry.
  • April 2010, Graduate algebraic geometry working seminar, Higher-dimensional algebraic geometry: flips and flops in variational GIT.
  • April 2010, Graduate algebraic geometry working seminar, Higher-dimensional algebraic geometry: uniruled and rationally conected varieties.
  • April 2010, Graduate algebraic geometry working seminar, Higher-dimensional algebraic geometry: "bend-and-break" lemmas II.
  • April 2010, Graduate algebraic geometry working seminar, Higher-dimensional algebraic geometry: "bend-and-break" lemmas I.
  • March 2010, Graduate algebraic geometry working seminar, Divisors and 1-cycles, intersection numbers, and cone of curves.
  • March 2010, Graduate algebraic geometry working seminar, Higher-dimensional algebraic geometry: parameterizing morphisms.
  • February 2010, Graduate AG working seminar, Higher order deformation and obstruction theory applied to subschemes, invertible sheaves, vector bundles, and coherent sheaves.
  • January 2010, Graduate algebraic geometry working seminar, Deformation theory and higher dimensional algebraic geometry: understanding first order deformation.
  • February 2010, AWM-Illinois, Introduction to intersection theory.
  • February 2009, AWM-Illinois, On algebraic surfaces.
  • April 2008, Graduate geometry & topology, Groebner bases, Hilbert basis theorem, and Buchberger's algorithm.
  • February 2008, AWM-Illinois, Geometric invariants of blow-ups and del Pezzo surfaces.

Other professional training.

  • Faculty development workshop, with the Department of Mathematical Sciences, United States Military Academy.
  • Algebra research group funded by Vertical Integration of Research and Education in the mathematical sciences, with Brian Boe, Lenny Chastkofsky, and Dan Nakano, Department of Mathematics.
  • Mathematica programming to study Lie algebra cohomology, with Lenny Chastkofsky, Department of Mathematics.
  • Learning and Performance Support Laboratory, with Chandra Orrill, Professional Development.
  • Use nonstandard analysis to study Hausdorff measure and fractals of dimension less than 1, MPhil thesis at UBham, with Richard Kaye, Department of Mathematics.
  • Use Monte Carlo methods to study surface properties of Silicon-Germanium atoms (semiconductors) in a fixed volume system, undergraduate REU at UGA, with David P Landau, Department of Physics.
  • Green's conjecture in low characteristics, undergraduate REU at UGA, with Bill Rulla, Department of Mathematics.
  • Theoretical physics research, undergraduate research at UGA, Department of Physics, Declined, schedule conflict, Department of Physics.
  • Singularities and desingularization, undergraduate REU at UGA, with Elham Izadi, Department of Mathematics.

Codes

KLR-algebras, with Peter McNamara, Travis Scrimshaw, Peter Tingley, etc. Implement KLR-algebras, related algebras, and their representations in sage/python.

Teaching Experience

United States Military Academy.

  • MA206, Probability and Statistics, Fall 2018, instructor.
  • MA206, Probability and Statistics, Fall 2018, instructor.
  • MA206, Probability and Statistics, Fall 2018, instructor.
  • MA206, Probability and Statistics, Fall 2018, instructor.
  • MA206, Probability and Statistics, Maymester 2018, instructor.
  • MA487, Mathematical Analysis II, Fall 2017, instructor and course director.
  • MA206, Probability and Statistics, Fall 2017, instructor.
  • MA206, Probability and Statistics, Fall 2017, instructor.
  • MA255, Advanced Multivariable Calculus, Spring 2017, instructor.
  • MA255, Advanced Multivariable Calculus, Spring 2017, instructor.
  • MA255, Advanced Multivariable Calculus, Spring 2017, instructor.
  • MA499, Senior Honors Thesis: Paper and Defense, Spring 2017, adviser.
  • MA383, A Transition to Advanced Mathematics, Fall 2016, instructor and course director.
  • MA383, A Transition to Advanced Mathematics, Fall 2016, independent study director.
  • MA206, Probability and Statistics, Fall 2016, instructor.
  • MA498, Senior Honors Thesis: Research and Proposal, Fall 2016, adviser.
  • MA206, Probability and Statistics, Maymester 2016, instructor.
  • MA206, Probability and Statistics, Spring 2016, instructor.
  • MA206, Probability and Statistics, Spring 2016, instructor.
  • MA206, Probability and Statistics, Spring 2016, instructor.
  • MA206, Probability and Statistics, Spring 2016, instructor.
      • We will use R, Excel, and Mathematica on a regular basis. Applications toward geometry and measure theory will be discussed on a regular basis.
  • MA499, Senior Honors Thesis: Paper and Defense, Spring 2016, adviser.
  • MA103, Discrete Dynamical (homogeneous and inhomogeneous, linear and nonlinear, discrete and continuous) Systems and Introduction to Calculus, Fall 2015, instructor.
  • MA103, Discrete Dynamical Systems and Introduction to Calculus, Fall 2015, instructor.
  • MA103, Discrete Dynamical Systems and Introduction to Calculus, Fall 2015, instructor.
      • Periodic robotics lab demonstrations for cadets in MA103, together with applications in physics, engineering, and graph theory (network centrality, cryptology, Markov chains).
      • We use Excel and Mathematica on a regular basis to develop fundamental skills to solve interdisciplinary (operations research) problems.
  • MA498, Senior Honors Thesis: Research and Proposal, Fall 2015, adviser.

University of Illinois at Urbana-Champaign.

  • Math 241, Calculus III: Multivariable Calculus, Fall 2012, multiple discussion sections.
  • Math 220, Calculus & Mathematica: Single Variable Calculus, Fall 2011, instructor.
  • Math 231, Calculus II: Sequences and Series, Spring 2011, discussion section.
  • Math 125, Linear Algebra, Fall 2010, instructor for a large lecture.
  • Math 415, Linear Algebra, Spring 2010, grader for multiple sections.
  • Math 241, Merit Calculus III: Multivariable Calculus, Fall 2009, multiple discussion sections.
  • Math 241, Merit Calculus III: Multivariable Calculus, Spring 2009, multiple discussion sections.
  • Math 241, Calculus III: Multivariable Calculus, Fall 2008, multiple discussion sections.
  • Math 347, Problem Solving and Introduction to Proofs, Summer 2008, grader and led discussions.
  • Math 231, Calculus II: Sequences and Series, Spring 2008, tutor for 4 evenings a week.
  • Math 125, Linear Algebra, Spring 2008, grader for multiple sections.
  • Math 234, Business Calculus I: Single Variable Calculus, Fall 2007, multiple discussion sections.
  • Math 115, Math 220, Math 221, Math 231, Math 241, Math 415, tutor.
  • Math 362/ECE 313, Probability with Engineering Applications, tutor.
  • ECE 310/410, Digital Signal Processing, tutor.
  • Phys 508, Mathematical Methods in Physics, tutor.
  • High school (proof based) geometry, tutor.
  • Advanced Placement BC Calculus, tutor.

University of Birmingham, United Kingdom.

  • MSM1Da and MSM1Db, Applicable Mathematics A and B, course assistant.
  • Drop-in tutoring for all courses, two days a week.
  • MSM1Xa, The Impact of Mathematics A, course assistant.
  • MSM2Ca, Linear Algebra A, course assistant.
  • MSM1Ab, Mathematical Physics B, course assistant.
  • MSM2Bb, Real and Complex Variable Theory B, course assistant.
  • MSM2O2b, Statistics II B, course assistant.

University of Georgia.

  • Math 5210/7210, Euclidean and non-Euclidean Geometry, course assistant.
  • Phys 1112, Introduction to Electricity and Magnetism II, lab assistant.
  • Math 2700, Partial Differential Equations, grader.

Research Students

United States Military Academy.

  • Anton Nelson, pure mathematics research student, 2017-2018.
    • Currently studying invariants of knot theory using skein relations and Chern-Simons theory.
  • Nicolette (Nikki) Marie Jimenez, Bachelor of Science in Mathematics, with Honors, 2016-2017.
    • Thesis: Constructing symplectic varieties.
    • Research Assistant, Applied Physics Laboratory, Johns Hopkins University, declined.
    • Federal advisory consultant, analytics division, Deloitte, Washington D.C., 2017-current.
  • Lisa Marie Jones, Bachelor of Science in Mathematics, with Honors, 2015-2016.
      • Thesis: On invariants and semi-invariants of filtered quiver representations of k-Kronecker and n-Jordan quivers.
      • 2016 Winston Churchill Scholar, masters in pure mathematics at the University of Cambridge, 2016-2017.
      • U.S. Army, Operational Cyber Unit, 2017-2019.
      • 2016 NSF Graduate Research Fellow (3 years), doctoral studies in theoretical computer science at Harvard University, 2019-2022.

Service

  • Spring 2020, TBA, Brown University, Providence, RI.
  • Summer 2019, Co-organizer of FPSAC 2019 (Free and Practical Software for Algebraic Combinatorics), Ljubljana, Slovenia.
  • Spring 2019, Small group research co-leader for Women in Noncommutative Algebra and Representation Theory Workshop (WINART2), University of Leeds, England.
  • Fall 2018 to Present, Zentralblatt MATH, reviewer.
  • July 2018, Mathematical Sciences Research Institute (MSRI) Research Member.
  • 2017-2019, Advances in the Mathematical Sciences (Adv. Math. Sci.): Research from the 2017 AWM Symposium (Springer book), Program Committee chair, managing editor.
  • 2017-2019, Advances in the Mathematical Sciences (Adv. Math. Sci.): Research from the 2017 AWM Symposium (Springer book), reviewer and referee.
  • April 2017, AWM-UCLA, University of California, Los Angeles, CA, poster judge.

United States Military Academy.

  • Course Director for MA487: Analysis II (Differential Geometry), Fall 2017.
  • Summer Leaders Experience, June 2017.
  • Working seminar on D-modules organizer, Spring 2017.
  • Independent Reader (Thesis Examiner): Modeling deterrence strategy, 2016-2017.
  • Independent Reader (Thesis Examiner): Generalizing Zeckendorf's theorem via bin sequences, 2016-2017.
  • Independent Reader (Thesis Examiner): Exploring topological data analysis through discrete signal data sets, 2016-2017.
  • Sonia Kovalevsky Day Workshop Instructor, 2016-2017.
  • (Academic) Officer in Charge (OIC), April 7-10, 2017.
  • Drones Workshop Outreach at West Point, NY, Dec 2016.
  • Course Director for MA383: A Transition to Advanced Mathematics, Fall 2016.
  • Independent Reader (Thesis Examiner): Implementing an anomaly-based intrusion detection system utilizing statistical modeling-focus on internal threat, 2015-2016.
  • Independent Reader (Thesis Examiner): A Markov Chain Monte Carlo simulation to predict baseball outcomes and baseball bets, 2015-2016.
  • (Academic) Officer in Charge (OIC), April 15-17, 2016.
  • Academic Officer in Charge (AOIC), November 8, 2015.
  • Phi Kappa Phi (Mathematics Honors Society) organizer, 2015-2018.
  • Mathematica Militaris editor and reviewer, 2015-2018.
  • Implementing a robotics laboratory in a curriculum, 2015-2016.

University of Illinois at Urbana-Champaign.

Coming soon.

University of Birmingham, England.

Coming soon.

University of Georgia.

Coming soon.

Conferences, Workshops, and Research Visits

Research Visitors

If you'd like to meet any of the research visitors, please contact me.

  • TBA, United States Military Academy, D. Swinarski, Fordham University, Professor.
  • TBA, United States Military Academy, E. Norton, Universitat Bonn, Postdoc.
  • TBA, United States Military Academy, Venkat Dasari, U.S. Army Research Laboratory, Researcher.
  • TBA, United States Military Academy, Zajj Daugherty, City College of New York, Assistant Professor.
  • Fall 2018, United States Military Academy, Michał Zakrzewski, Jan Kochanowski University, Kielce, Poland, Assistant Professor.
  • Fall 2018, United States Military Academy, Chun-Ju Lai, University of Georgia, Postdoc.
  • Fall 2018, United States Military Academy, Jieru Zhu, State University of New York at Buffalo, Postdoc.
  • Oct 28-Nov 3, 2018, United States Military Academy, Travis Scrimshaw, University of Minnesota, Postdoc.
  • July 29-Aug 2, 2018, United States Military Academy, Ola Amara Omari, Bar-Ilan University, Ramat Gan, Israel, Graduate Student.
  • July 29-Aug 2, 2018, United States Military Academy, Malka Mary Schaps, Bar-Ilan University, Ramat Gan, Israel, Professor and Former Dean.
  • July 29-Aug 2, 2018, United States Military Academy, Dani (Danny) Neftin, Technion – Israel Institute of Technology, Haifa, Israel, Assistant Professor.
  • July 29-Aug 2, 2018, United States Military Academy, Shifi Reif, Bar-Ilan University, Ramat Gan, Israel, Assistant Professor.
  • May 23, 2018, United States Military Academy, Nikki Jimenez, Deloitte, Washington D.C, Federal Advisory Consultant.
  • March 28, 2018, United States Military Academy, Mary Lynn Reed, Department of Defense, Chief of Mathematics Research.
  • November 2, 2017, United States Military Academy, Mikhail Khovanov, Columbia University, Professor.
  • October 2, 2017, United States Military Academy, Keith Weinstein, Google, Network Engineer.
  • September 2, 2017, United States Military Academy, Michał Zakrzewski, Jan Kochanowski University, Kielce, Poland, Assistant Professor.
  • April 11-12, 2017, United States Military Academy, Mary Lynn Reed, Department of Defense, Chief of Mathematics Research.
  • April 4-5, 2017, United States Military Academy, Thomas Nevins, University of Illinois at Urbana-Champaign, Professor.
  • February 19-23, 2017, United States Military Academy, Malka Mary Schaps, Bar-Ilan University, Ramat Gan, Israel, Professor and Former Dean.
  • September 6, 2016, United States Military Academy, Lisa Jones, University of Cambridge, Cambridge, England, Graduate Student.
  • September 3-6, 2016, United States Military Academy, Jon Oh, Emerson, Engineer and Project Leader.
  • October 15-20, 2015, United States Military Academy, Ben Cox, College of Charleston, Professor.
  • August 7, 2015, United States Military Academy, Kyu-Hwan Lee, University of Connecticut, Professor.
  • March 21-22, 2015, University of Illinois, Angela Wu, University of Chicago, Graduate Student.
  • December 7-11, 2014, University of Illinois, Angela Wu, University of Chicago, Graduate Student.

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

A Mathematician's Apology, by G. H. Hardy


Mathematics is the most beautiful and most powerful creation of the human spirit.

Stefan Banach