# Mee Seong Im

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

Stefan Banach

**Assistant Professor**

**Chauvenet Hall, Office 342**

**Department of Mathematics**

**United States Naval Academy**

**Annapolis, MD 21402**

**Office: (410) 293-6776**

Email: im [at] usna [dot] edu

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 **Tenure-Track Assistant Professor** at the United States Naval Academy in Annapolis, MD effective July 6, 2020.

In Fall of 2020, I will teach 2 sections of SM122: Calculus II.

**Co-organizer**: I am organizing a special session at the University of Utah in Salt Lake City.

Geometry and Representation Theory of Quantum Algebras and Related Topics

Co-organizers: Bach Nguyen, Arik Wilbert.

**Co-organizer**: I am organizing Sage Day for July 2020 at Bar-Ilan University in Ramat Gan, Israel. [**CANCELLED**]

Co-organizers: Tomer Bauer and Travis Scrimshaw, with support from OpenDreamKit, the Horizon 2020 European Research Infrastructures project #676541.

**Co-organizer**: I have organized two special sessions at the University of California at Riverside.

Geometric Methods in Representation Theory

Co-organizers: Neal Livesay, Daniel Sage.

Geometry and Representation Theory of Quantum Algebras and Related Topics

Co-organizers: Bach Nguyen, Hans Nordstrom, Karl Schmidt.

**Co-organizer**: I have organized FPSAC Sage Days 2019 for July 8-12, 2019 at the University of Ljubljana, Slovenia.

Co-organizers: Matjaž Konvalinka, Ben Salisbury, Nicolas Thiéry, and Bruce Westbury.

**Reviewer**: I am a reviewer for Zentralblatt MATH (ID: 17038) and Mathematical Reviews (ID: 139834).

**Editorial Manager**: I am an Editorial Manager and a reviewer for Journal of Geometry and Physics and Linear Algebra and its Applications.

## Research Interests

**Diagrammatic algebras and categorification**. Quiver Hecke algebras, modified Hecke algebras, quantum group, variations of Brauer algebras, Temperley-Lieb algebras.**Geometric constructions**. Fiber bundles, Hilbert schemes and moduli spaces.**Equivariant geometry**of algebraic groups, Lie algebras and superalgebras, (Grothendieck-)Springer resolutions, (exotic) Springer fibers, 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 a certain bases of Lie superalgebra (tentative title), in progress.

On cohomological properties of quiver flag varieties (tentative title), in progress.

Certain holomorphic line bundles (tentative title), with M. Zakrzewski, in progress, 2020.

On certain Lie superalgebras (tentative title), with E. Norton and B. Westbury, in progress, 2020.

Natural transformations between induction and restriction on iterated symmetric group products, with C. Ozan Oguz, in preparation, 2020.

On certain invariants of a Lie superalgebra (tentative title), in preparation, 2020.

Quantum groups and colored HOMFLY-PT invariants (tentative title), in preparation, 2020.

Genetic optimization algorithms applied toward mission computability models, with V. Dasari, 88th MORS Symposium: AI and Autonomous Systems

**WG35**(2020), 1-11.Towards the affine and geometric invariant theory quotients of the Borel moment map, with M. Tosun, preprint (2020), 12 pages.

Monte Carlo methods on a fixed volume system of Silicon-Germanium atoms, Proc. SPIE

**11410**-29 (2020), 1-11.Suggestions to study affine and GIT quotients of the extended Grothendieck-Springer resolution, submitted, Sugaku (2019), 11 pages.

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. (2019), 15 pages.A short proof on the transition matrix from the Specht basis to the Kazhdan-Lusztig basis,

**accepted**upon revision, Rocky Mountain J. Math. (2019), 7 pages.Nonstandard approach to Hausdorff outer measure, submitted, Math. Student (2019), 9 pages.

The Grothendieck ring of the periplectic Lie supergroup and supersymmetric functions, with S. Reif and V. Serganova, submitted, Sém. Lothar. Combin. (2019), 12 pages.

Solving machine learning optimization problems using quantum computers, with L. Beshaj and V. Dasari, Proc. SPIE

**11419**-16 (2020), 1-10.Transitioning between tableaux and spider bases for Specht modules, with J. Zhu,

**under revision**, Algebr. Represent. Theory (2019), 21 pages.Irreducible components of two-row Springer fibers and Nakajima quiver varieties, with C.-J. Lai and A. Wilbert, preprint (2019), 38 pages.

Denominator identities for the periplectic Lie superalgebra, with C. Hoyt and S. Reif, submitted, Transform. Groups (2019), 12 pages.

Irreducible calibrated representations of periplectic Brauer algebras and hook representations of the symmetric group, with E. Norton, J. Algebra

**560**(2020), 442-485.Grothendieck rings of periplectic Lie superalgebras, with S. Reif and V. Serganova,

**accepted**, Math. Res. Lett. (2019), 15 pages.On calibrated representations of the degenerate affine periplectic Brauer algebra, with Z. Daugherty, I. Halacheva, and E. Norton,

**accepted**upon minor revision, Surv. Math. Appl. (2019), 11 pages.The regularity of almost-commuting partial Grothendieck--Springer resolutions and parabolic analogs of Calogero--Moser varieties, with T. Scrimshaw, J. Lie Theory

**31**(2021), no. 1, 22 pages.On the module structure of the center of hyperelliptic Krichever-Novikov algebras II, with B. Cox, X. Guo, K. Zhao, Comm. Alg.

**47**(2019), no. 12, 5142-5163.Advances in the Mathematical Sciences, with A. Deines, D. Ferrero, E. Graham, C. Manore, C. Price, Springer International Publishing Switzerland

**15**(2018), XIV, 1-270.Optimization problems with low SWaP tactical Computing, with V. Dasari, L. Beshaj, and D. Shires, Proc. SPIE

**11013**-G (2019), 1-8.Beta super-functions on super-Grassmannians, with M. Zakrzewski, Lett. Math. Sci.

**1**(2018), no. 1, 41-60.Categorification of Verma modules and indecomposable projective modules in the category I_g(sl(2)) for sl(2), with B. Cox, submitted, J. Phys. A (2018), 23 pages.

Complexity and mission computability of adaptive computing systems, with V. Dasari and B. Geerhart, J. Defense Modeling & Simulation

**17**(2019), no. 1, 1-7.Optimization and synchronization of programmable quantum communication channels, with V. Dasari, Proc. SPIE

**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, Selecta Math.

**26**(2020), no. 2, 42 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, Math. Res. Lett.

**26**(2019), no. 3, 643-710.The regular semisimple locus of the affine quotient of the cotangent bundle of the Grothendieck-Springer resolution, J. Geom. Phys.

**132**(2018), 84-98.Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence, with A. Wu, Adv. Math. Sci.

**15**(2018), 29-46.Generalized iterated wreath products of cyclic groups and rooted trees correspondence, with A. Wu, Adv. Math. Sci.

**15**(2018), 15-28.Unipotent invariants of filtered representations of quivers and the isospectral Hilbert scheme, with L. Jones, arXiv: 1608.02293, preprint (2016), 22 pages.

Families of orthogonal Laurent polynomials, hyperelliptic Lie algebras and elliptic integrals, with B. Cox, Integral Transforms Spec. Funct.

**27**(2016), no. 11, 899-919.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.Semi-invariants of filtered quiver representations with at most two pathways, arXiv: 1409.0702, preprint (2014), 11 pages.

The regularity of the cotangent bundle of the Grothendieck-Springer resolution, article (2013), 3 pages.

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.

## Selected Research Slides

Nov 2019,

**Nakajima quiver varieties and irreducible components of Springer fibers I**Geometric Methods in Rep. Thy., Dept. of Math., Univ. of California, Riverside, CA. [shorter version, slides]

Nov 2019,

**The geometry of parabolic Hamiltonian reduction**Canonical Bases, Cluster Str. & Non-Comm. Birational Geom., Univ. of California, Riverside, CA. [slides]

Nov 2019,

**Towards quantization of degenerate affine Brauer superalgebras**Geometry and Rep. Thy. of Quantum Algs. & Related Topics, Univ. of California, Riverside, CA. [slides]

May 2019,

**The geometry of parabolic Hamiltonian reduction**Geom. & Categorical Rep. Thy., Southeastern Lie Theory XI, Louisiana State Univ., Baton Rouge, LA. [slides]

Apr 2019,

**Optimization problems with low SWAP tactical computing platforms**SPIE Defense & Security: Disruptive Tech. in Inform. Sci., Baltimore Conv. Center, Baltimore, MD. [slides]

Apr 2019,

**The geometry of Borel Hamiltonian reduction**

Rep. Thy. of Quantum Algebras and Related Topics, Univ. of Connecticut, Hartford, CT. [slides]

Apr 2019,

**Natural transformations between induction and restriction on iterated symm. group algebras**Texas-Oklahoma Reps. and Automorphic Forms X, Univ. of North Texas, Denton, TX. [slides]

Apr 2019,

**The Grothendieck ring of the periplectic Lie superalgebra**Texas-Oklahoma Representations and Automorphic Forms X, Univ. of North Texas, Denton, TX. [poster]

Mar 2019,

**The reduced Grothendieck ring of the periplectic Lie superalgebra**University of Hawaii at Manoa, Honolulu, Hawaii. [slides]

Oct 2018,

**Representations of degenerate affine Brauer superalgebras**San Francisco State University, San Francisco, CA. [slides]

Oct 2018,

**A geometric construction of beta super-functions on super-Grassmannians**26th ARL-USMA Technical Symposium, Aberdeen Proving Ground, MD. [slides]

July 2018,

**A construction of the affine VW supercategory**ICERM, Brown University, Providence, RI. [slides]

June 2018,

**An investigation towards higher Schur-Weyl duality for the periplectic Lie superalgebra**Colorado State University Mountain Campus, Bellvue, CO. [slides]

June 2018,

**On the affine VW supercategory**Department of Mathematics, University of Georgia, Athens, GA. [slides]

May 2018,

**On the representation theory of periplectic Lie superalgebras and affine VW supercategory**Department of Mathematics, Jan Kochanowski University, Kielce, Poland. [slides]

Apr 2018,

**Synchronization of programmable quantum and classical communication channels**Apr 2018,

**On the affine VW supercategory**Department of Mathematics, University of Oklahoma, Norman, OK. [slides]

Mar 2018,

**On a construction of the affine VW supercategory**Ohio State University, Columbus, OH. [slides]

Dec 2017,

**On higher cohomology vanishing for quiver flag varieties**Department of Mathematics, Virginia Tech, Blacksburg, VA. [slides]

Oct 2017,

**A 1-categorification of Verma modules for sl(2)**25th ARL-USMA Technical Symposium, Aberdeen Proving Ground, MD. [poster]

Jul 2017,

**Cohomological properties of certain quiver flag varieties**College of Science and Technology, Temple University, Philadelphia, PA. [slides]

Jul 2017,

**The category of finite-dimensional representations of periplectic Lie superalgebras**Lev Campus of the Jerusalem College of Technology, Jerusalem, Israel. [slides]

Jul 2017,

**On the finite-dimensional periplectic Lie superalgebra representations**Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel. [slides]

May 2017,

**The category of finite-dim'l integrable reps. of the periplectic Lie superalgebra p(n)**University of Reims Champagne-Ardenne, Moulin de la Housse, Reims, France. [poster]

Apr 2017,

**Representations of signed affine Brauer algebras**University of California-Los Angeles, Los Angeles, CA. [slides]

Apr 2017,

**Representations of affine Nazarov-Wenzl algebras**Department of Mathematics, Oklahoma State University, Stillwater, OK. [slides]

Jan 2017,

**Higher Schur-Weyl duality for Lie superalgebras**Joint Mathematics Meeting (Lie supersubalgebras), Atlanta, GA. [slides]

Jan 2017,

**On the geom. of filtered reps. of quivers and connections to isospectral Hilb. schemes**Joint Mathematics Meeting (geometry), Atlanta, GA. [slides]

Mar 2016,

**A categorification of sl(2)-Verma modules**AMS Sectional Meeting, University of Georgia, Athens, GA. [slides]

Jan 2016,

**On the categorification of Verma modules for sl(2)**Joint Mathematics Meeting, Seattle, WA. [slides]

Oct 2015,

**On families of orthogonal Laurent poly., hyperelliptic Lie superalg. and elliptic integrals**Army Research Lab, Aberdeen Proving Ground, MD. [slides]

May 2015,

**From a quantum field theory to categorical representation theory**Pomona College, Claremont, CA. [slides]

Apr 2015,

**The geometric construction of KLR-algebras**Florida Gulf Coast University, Fort Myers, FL. [slides]

Apr 2015,

**On quiver Hecke, quantum shuffle, and quantum cluster characters**University of Maryland, College Park, MD. [poster]

Jan 2015,

**Quiver Hecke algebras and filtered quiver representations**Joint Mathematics Meeting, San Antonio, TX. [slides]

May 2014,

**On constr. inv. for gen. quiv. var. with appl. to shape deform. in target & activity recognition**Center for Naval Analyses, Alexandria, VA. [slides]

Apr 2014,

**On filtered reps. of quiv. with at most two pathways & on the generalized GS resolution**University of California, Berkeley, CA. [slides]

Apr 2014,

**On semi-inv. of filt. reps. of quiv. and the cotang. bdle. of the enhanced GS resolution**Doctoral defense, University of Illinois, Urbana, IL. [slides]

Dec 2013,

**Applications of filtered quiver varieties in representation theory**MIT Lincoln Laboratory, Lexington, MA. [slides]

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

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