Lie Theory Math

**Renowned Mathematician Dr. Mark Sepanski on Lie Theory**

Lie Theory Math

**Blending algebra**, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Included is the construction of the Spin groups, Schur Orthogonality, the Peter–Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel–Weil Theorem. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups. (From Mark’s Book)

# Mark Sepanski

Professor of Mathematics

Graduate Program Director[email protected]Sid Richardson 302E(254) 710-6580 (email preferred)**Professor of Mathematics**

**Education:**

Ph.D. Mathematics, MIT, 1990-1994 (Advisor: B. Kostant)

B.S., Mathematics, Purdue University, 1987-1990

**Biography:**

Though born in Minnestoa and ending up in Indiana, Dr. Sepanski mostly grew up in Wisconsin. He has been married to Laura Sepanski since 1990 and has three delightful children: Sarah, Benjamin, and Shannon.

Dr. Sepanski earned a Ph.D. in Mathematics from MIT in 1994. He had postdoctoral positions at Cornell University and Oklahoma State University and spent a semester at the Mathematical Sciences Research Institute in Berkeley.

He’s been with Baylor University since 1997 where he is a Professor of Mathematics and Graduate Program Director.

For hobbies, Dr. Sepanski spent many years hiking, rock climbing, earning a black belt in taekwondo, gardening with native Texas plants, and running. Currently, he is into board games, bike riding, cooking, fine drinks, and traveling. He loves fantasy and science fiction and, most of all, spending time with his wife and three children.

**Academic Interests and Research:**

Dr. Sepanski does research in Representation Theory, Lie Theory, and Combinatorics and has written many papers in theoretical mathematics as well as two books, *Compact Lie Groups* and *Algebra*.

He is also active in mathematics education and serves on the Mathematics Advisory Group for Graduate Education with TPSEMath (Transforming Post-Secondary Education in Mathematics), as well as serving with the Math Alliance (an organization devoted to helping underrepresented students earn doctoral degrees in mathematical sciences).

**Selected Research Articles:**

Schrödinger-type equations and unitary highest weight representations of U(n; n), joint with M. Huziker and R. Stanke, J. Lie Theory., 30 (2020), no. 1, 201-222.

Lyndon word decompositions and pseudo orbits on q-nary graphs, joint with R. Band and J. Harrison, J. Math. Anal. Appl., 470 (2019), no. 1, 135–144.

Schrödinger-type equations and unitary highest weight representations of the metaplectic group, joint with M. Hunziker and R. Stanke, Representation theory and harmonic analysis on symmetric spaces, 157–174, Contemp. Math., 714, Amer. Math. Soc., Providence, RI, 2018.

Net regular signed trees, joint with I. Michael, *Australas. J. Combin. 66* (2016), 192-204.

A system of Schrödinger equations and the oscillator representation, joint with M. Hunziker and R. Stanke, *Electron. J. Differential Equations 2015*, No. 260, 28 pp.

On divisibility of convolutions of central binomial coefficients, *Electron. J. Combin. 21* (2014), no. 1, Paper 1.32, 7 pp.

The minimal representation of the conformal group and classical solutions to the wave equation, joint with M. Hunziker and R. Stanke, *J. Lie Theory 22* (2012), no. 2, 301-360.

Global Lie symmetries of the heat and Schrödinger equation, joint with R. Stanke, *J. Lie Theory 20* (2010), no. 3, 543-580.

Distinguished orbits and the L-S category of simply connected compact Lie groups, joint with M. Hunziker, *Topology Appl. 156* (2009), no. 15, 2443-2451.

Positivity of zeta distributions and small unitary representations, joint with L. Barchini and R. Zierau, In: The ubiquitous heat kernel, 1-46, *Contemp. Math. 398*, Amer. Math. Soc., Providence, RI, 2006.

On SL(2,**R**) Lie symmetries and representation theory, joint with R. Stanke, *J. Funct. Anal. 224 *(2005), 1-21.

Infinite commutative product formulas for relative extremal projectors, joint with C. Conley, *Adv. Math. 196* (2005), 52-77.

Singular projective bases and the generalized Bol operator, joint with C. Conley, *Adv. Appl. Math. 33* (2004), 158-191.

K-types of SU(1,n) representations and restriction of cohomology, *Pacific J. Math. 192* (2000), 385-398.

Block-compatible metaplectic cocycles, joint with W. Banks and J. Levy, *J. Reine Angew. Math. 507* (1999), 131-163.

Closure ordering and the Kostant-Sekiguchi correspondence, joint with D. Barbasch, *Proc. Amer. Math. Soc. 126* (1998), 311-317.

L_2(q) and the rank two Lie groups: their construction in light of Kostant’s conjecture, *Trans. Amer. Math. Soc. 347* (1995), no. 10, 3983-4021.

**Books:**

*Algebra*, Pure and Applied Undergraduate Texts, 11, American Mathematical Society, 2010.

*Compact Lie Groups*, Graduate Texts in Mathematics, 235, Springer-Verlag, 2007.

**Ph.D. Students:**

- Jose Franco
- John Miller (joint with M. Hunziker)

**Teaching Interests:**

Dr. Sepanksi’s teaching interests range from introductory calculus classes for undergraduates to specialized courses for Ph.D. students.

**Courses taught at Baylor:**

- MTH 1304 – Pre-Calculus
- MTH 1321 – Calculus I
- MTH 1322 – Calculus II
- MTH 2311 – Linear Algebra
- MTH 2321 – Calculus III
- MTH 3312 – Foundations of Combinatorics and Algebra
- MTH 3323 – Introduction to Analysis
- MTH 3325 – Ordinary Differential Equations
- MTH 4314 – Abstract Algebra
- MTH 4326 – Advanced Calculus I
- MTH 4327 – Advanced Calculus II
- MTH 5310 – Advanced Abstract Algebra I
- MTH 5311 – Advanced Abstract Algebra II
- MTH 5323 – Theory of Functions of Real Variables I
- MTH 5324 – Theory of Functions of Real Variables II
- MTH 5330 – Topology
- MTH 5331 – Algebraic Topology I
- MTH 5332 – Algebraic Topology II
- MTH 5340 – Differential Geometry
- MTH 5350 – Complex Analysis
- MTH 6340 – Compact Lie Groups
- MTH 6341 – Lie Algebras
- MTH 6V43 – Advanced Topics in Representation Theory

**YouTube:**

Math Videos and Help: https://www.youtube.com/channel/UCIUFPD3KRnry64a77XTyDPw

**LinkedIn:**

Lie Theory Math