# Mee Seong Im

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

Stefan Banach

**Assistant Professor**

**Chauvenet Hall, Office 342**

**United States Naval Academy**

**572C Holloway Road**

**Annapolis, MD 21402-5002**

**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 an **Assistant Professor** at the United States Naval Academy in Annapolis, MD.

In Fall of 2021, I am teaching:

2 sections of

**SM221P****Calculus III****with****vector****fields****for****plebes (****freshmen****)**,Section 3041 MWRF3 (0955-1045): CH175,

Section 4041 MWRF4 (1055-1145): CH175.

1 section of

**SM362****Modern****Algebra**,Section 5001 MWF5 (1330-1420): CH175.

1 section of

**SM485****Reading****Course****: Algebraic Topology and Quantum Field Theory**,Section 5241 TR5 (1330-1420), R6 (1430-1520): CH103.

In Spring of 2022, I am expected to teach 2 sections of **SM219** **Introduction to Statistics** (**Data Science**).

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

**Organizer**: I am organizing a special session for 2022 AWM Research Symposium at the Institute for Mathematics and its Applications, in partnership with the University of Minnesota on June 16-19, 2022.

**Geometric****and****Categorical****Aspects****of****Representation****Theory****and****Related****Topics**.

**Co-organizer**: I am organizing a special session at the University of South Alabama in Mobile, AL, which will take place on Nov 20-21, 2021.

**Geometric****and****Algebraic****Aspects**of Quantum Groups and Related TopicsCo-organizers: Bach Nguyen, Arik Wilbert. [

**Mee Seong Im**,**Point of Contact, but feel free to contact any of us**]

**Co-organizer**: I have organized a special session at San Francisco State University in San Francisco, which took place on May 1-2, 2021 (virtual).

Categorical and Combinatorial Methods in Representation Theory, and Related Topics

Co-organizers: Bach Nguyen, Arik Wilbert.

**Co-organizer**: I have organized a special session at the University of Utah in Salt Lake City, which took place on Oct 24-25, 2020 (virtual).

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, which took place on Nov 9-10, 2019.

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 at the University of Ljubljana, Slovenia, which took place on July 8-12, 2019.

Co-organizers: MatjaĹľ Konvalinka, Ben Salisbury, Nicolas ThiĂ©ry, and Bruce Westbury.

**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's supervision.

Tom Nevins's Memorial Lecture from Friday June 11, 2021.

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, 2021.

On certain Lie superalgebras (tentative title), with E. Norton and B. Westbury, in progress, 2021.

On certain invariants of a Lie superalgebra (tentative title), in preparation, 2021.

Quantum groups and colored HOMFLY-PT invariants (tentative title), in preparation, 2021.

On certain properties of the periplectic Lie superalgebra (tentative title), with Shifra Reif, in progress, 2021.

Computational reduction of multilayer neural networks, with Venkat Dasari, preprint (2021), 1-10.

Foams, iterated wreath products, field extensions and Sylvester sums, with Mikhail Khovanov, submitted,

**under revision**, Theory Appl. Categ. (2021), 1-78.Natural transformations between induction and restriction on iterated wreath product of symmetric group of order 2, with Can Ozan Oguz, submitted, Represent. Theory (2021), 1-20.

One-dimensional topological theories with defects and linear generating functions, with Paul Zimmer,

**accepted**, Involve (2021), 1-14.Irreducible components of two-row Springer fibers for all classical types, with Chun-Ju Lai and Arik Wilbert,

**accepted**upon minor revision, Proc. Amer. Math. Soc. (2020), 1-14.Springer fibers via quiver varieties using Maffei--Nakajima isomorphism, with Chun-Ju Lai and Arik Wilbert,

**accepted**, J. Algebra (2021), 1-23.Genetic optimization algorithms applied toward mission computability models, with Venkat 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 Meral Tosun, preprint (2020), 1-12.

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, Surv. Math. Appl. (2019), 1-16.

Examples relating to Green's conjecture in low characteristics and genera, with Topik Teguh Estu, Justin Manning, Zachary Michaels, Jason Pasko, William Rulla and Nishan Wijesinghe, article (2019), 1-15.

A short proof on the transition matrix from the Specht basis to the Kazhdan-Lusztig basis,

**accepted**, Rocky Mountain J. Math. (2021), 1-7.Nonstandard approach to Hausdorff outer measure, Math. Student

**90**(2021), nos. 1-2, 1-9.The Grothendieck ring of the periplectic Lie supergroup and supersymmetric functions, with Shifra Reif and Vera Serganova, submitted, SĂ©m. Lothar. Combin. (2019), 1-12.

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

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

**accepted**, Algebr. Represent. Theory (2019), 1-13.Irreducible components of two-row Springer fibers and Nakajima quiver varieties, with Chun-Ju Lai and Arik Wilbert, preprint (2019), 1-38.

Denominator identities for the periplectic Lie superalgebra, with Crystal Hoyt and Shifra Reif, J. Algebra

**567**(2021), 459-474.Irreducible calibrated representations of periplectic Brauer algebras and hook representations of the symmetric group, with Emily Norton, J. Algebra

**560**(2020), 442-485.Grothendieck rings of periplectic Lie superalgebras, with Shifra Reif and Vera Serganova, Math. Res. Lett.

**28**(2021), no. 4, 1175-1195.On calibrated representations of the degenerate affine periplectic Brauer algebra, with Zajj Daugherty, Iva Halacheva, and Emily Norton, Surv. Math. Appl.

**16**(2021), 207-222.The regularity of almost-commuting partial Grothendieck--Springer resolutions and parabolic analogs of Calogero--Moser varieties, with Travis Scrimshaw, J. Lie Theory

**31**(2021), no. 1, 127-148.On the module structure of the center of hyperelliptic Krichever-Novikov algebras II, with Ben Cox, Xiangqian Guo, Kaiming Zhao, Comm. Alg.

**47**(2019), no. 12, 5142-5163.Advances in the Mathematical Sciences, with Alyson Deines, Daniela Ferrero, Erica Graham, Carrie Manore, Candice Price, Springer International Publishing Switzerland

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

**11013**-G (2019), 1-8.Beta super-functions on super-Grassmannians, with MichaĆš 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 Ben Cox, submitted, Missouri J. Math. Sci. (2018), 28 pages.

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

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

**10660**-26 (2018), 1-7.The affine VW supercategory, with Martina Balagovic, Zajj Daugherty, Inna Entova, Iva Halacheva, Johanna Hennig, Gail Letzter, Emily Norton, Vera Serganova and Catharina Stroppel, Selecta Math.

**26**(2020), no. 2, 42 pages.On the module structure of the center of hyperelliptic Krichever-Novikov algebras, with Ben 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 Martina Balagovic, Zajj Daugherty, Inna Entova, Iva Halacheva, Johanna Hennig, Gail Letzter, Emily Norton, Vera Serganova and Catharina 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 Angela Wu, Adv. Math. Sci.

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

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

Families of orthogonal Laurent polynomials, hyperelliptic Lie algebras and elliptic integrals, with Ben 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 Brian D. Boe, Leonard Chastkofsky, Daniel K. Nakano, Jonathan R. Kujawa, Emilie Wiesner, Irfan Bagci, Benjamin Connell, Bobbe J. Cooper, Wenjing Li, Kenyon J. Platt, Caroline B. Wright, Ben Wyser and Tyler 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 2021,

**Iterated wreath products and foams, with applications to field extensions, Sylvester sums, and matrix factorizations**ICERM, Brown University, Providence, RI. [slides]

Oct 2021,

**Grothendieck rings of periplectic Lie superalgebras**Southeastern Lie Theory Workshop XII, College of Charleston, Charleston, SC. [slides]

Oct 2021,

**Irreducible components of two-row Springer fibers for all classical types**Quiver representations: bridging theory and application, Creighton University, Omaha, NE. [slides]

Oct 2021,

**Singularities of the extended Grothendieck-Springer resolution**Algebra Seminar, Department of Mathematics, University of Virginia, Charlottesville, VA. [slides]

Sept 2021,

**Resolutions of singularities and geometric invariant theory**Pathways, Alphabet Inc., Google, Mountain View, CA and New York, NY. [notes]

Aug 2021,

**Explicit constructions of Hilbert schemes as blow-ups**Algebraic Geometry Research Community, American Institute of Mathematics, San Jose, CA. [notes]

Aug 2021,

**Singularities of a modification of the Grothendieck-Springer resolution**D-modules, Group Actions, and Frobenius: Computing on Singularities, ICERM, Brown University, Providence, RI. [slides]

Aug 2021,

**Singular varieties, symplectic resolutions, and Hilbert schemes**Algebraic Geometry Research Community, American Institute of Mathematics, San Jose, CA. [notes]

June 2021,

**Quantization appearing in geometry, algebra, topology, and communication channels**Women in Quantum, Quantum Week 2021, Seoul, South Korea. [slides]

June 2021,

**Irreducible components of two-row Springer fibers for all classical types**RepNet Virtual Seminar, International Centre for Mathematical Sciences, University of Edinburgh, Edinburgh, Scotland. [slides]

April 2021,

**Irreducible components of two-row Springer fibers for all classical types**Interactions between Representation Theory, Poisson Geometry, and Noncommutative Algebra, University of Cincinnati, Cincinnati, OH. [slides]

April 2021,

**Linearization, invariants, and categorification**Naval Academy Research Council Seminar (Academy-Wide), United States Naval Academy, Annapolis, MD. [slides]

Mar 2021,

**Denominator identities for the periplectic Lie superalgebra**Superalgebras, Quantum Groups, and Related Topics, Georgia Institute of Technology, Atlanta, GA. [slides]

Nov 2020,

**The geometry of parabolic Hamiltonian reduction**Combinatorics, Algebra, & Topology Seminar, United States Naval Academy, Annapolis, MD. [slides]

Aug 2020,

**Nakajima quiver varieties and irreducible components of Springer fibers**Representation Theory Seminar, Department of Mathematics, University of Massachusetts, Amherst, MA. [slides]

Nov 2019,

**Nakajima quiver varieties and irreducible components of Springer fibers I**Geometric Methods in Representation Theory, Department of Mathematics, Univ. of California, Riverside, CA. [shorter version, slides]

Nov 2019,

**The geometry of parabolic Hamiltonian reduction**Canonical Bases, Cluster Structures & Non-Commutative Birational Geometry, University of California, Riverside, CA. [slides]

Nov 2019,

**Towards quantization of degenerate affine Brauer superalgebras**Geometry and Representation Theory of Quantum Algebras & Related Topics, Univ. of California, Riverside, CA. [slides]

May 2019,

**The geometry of parabolic Hamiltonian reduction**Geometric & Categorical Representation Theory, 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 Technology in Information Sciences, Baltimore Conv. Center, Baltimore, MD. [slides]

Apr 2019,

**The geometry of Borel Hamiltonian reduction**

Representation Theory of Quantum Algebras and Related Topics, Univ. of Connecticut, Hartford, CT. [slides]

Apr 2019,

**Natural transformations between induction and restriction on iterated symmetric group algebras**Texas-Oklahoma Representations 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 representations 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 geometry of filtered representations 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 polynomials, hyperelliptic Lie superalgebras 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 constructing invariants for generalized quiver varieties with applications to shape deformation in target and activity recognition**Center for Naval Analyses, Alexandria, VA. [slides]

Apr 2014,

**On filtered representations of quivers with at most two pathways & on the generalized Grothendieck--Springer resolution**University of California, Berkeley, CA. [slides]

Apr 2014,

**On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced****Grothendieck-Springer****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