In Spring 2023, I will teach Advanced Linear Algebra, Math 404, MWF 11:20 - 12:50 in CW-331. The course webpage is here: Syllabus for Math 404 in Spring 2023.

My Office hours in Spring 2023 will be MWF 1:00 - 2:00 and by appointment. To schedule an appointment outside of my office hours, please send me an email at least 2 hours ahead of time.

I will continue to supervise the two honor societies I advise, Phi Beta Kappa and Pi Mu Epsilon. Induction ceremonies for these will be conducted in person in Spring 2023.

I taught Linear Algebra, Math 304, Section 5, MWF 2:50 - 4:20 in WH-G002, and I was the course coordinator for all six sections. The course webpage for all sections is: Syllabus for Math 304 in Fall 2022. and the webpage for my Section 5 was: Syllabus for Math 304-5 in Fall 2022.

I taught Number Systems, Math 330, Section 3, MWF 11:20 - 12:50 in WH-100B. The course webpage for my Section 3 was: Syllabus for Math 330-3 in Fall 2022.

In Spring 2022, I taught Advanced Linear Algebra, Math 404, MWF 11:20 - 12:50 in SL-206. The course webpage is here: Syllabus for Math 404 in Spring 2022.

I taught Linear Algebra, Math 304, Section 3, MWF 11:20 - 12:50 in WH-G002, and I was the course coordinator for all six sections. The course webpage for all sections was: Syllabus for Math 304 in Fall 2021. and the webpage for my Section 3 was: Syllabus for Math 304-3 in Fall 2021.

I taught Math 507, Linear Algebra and Matrix Theory, in Fall 2021, which met MWF 9:40 - 10:40 in WH-100E. A link to the syllabus is here: Syllabus for Math 507 in Fall 2021.

I was the course coordinator for eight sections of Math 304, Linear Algebra, and I taught Section 6, which met MWF 1:10 - 2:40 online through Zoom. The course webpage was: Syllabus for Math 304 in Spring 2021. I posted links to Panopto recordings of my online lectures, as well as pdf files of my written lecture notes on the webpage for my section 6, along with a detailed syllabus and advice here: Syllabus for Math 304-6 in Spring 2021.

I taught Math 507, Linear Algebra and Matrix Theory, in Fall 2020, which met MWF 10:50-11:50 online using Zoom. A link to the syllabus is here: Syllabus for Math 507 in Fall 2020.

I also taught Math 603, Lie Algebras, a topics course in Fall 2020, which met MWF 3:30-4:30 online using Zoom. Registered students received the Zoom link by email. A link to the syllabus is here: Syllabus for Math 603 in Fall 2020.

Here is a link to the Department of Mathematical Sciences RoundCube Mail Login.

I have a strong interest in sculptures, especially those related to mathematics, and I have made some in stone, bronze and wood. Here are links to webpages showing my work, and links to the artists who have inspired and influenced me. You can also follow the following link to an Artist's Statement Revised 2-1-2017 which I have written.

I am president of our local chapter of Phi Beta Kappa, Psi of New York. Phi Beta Kappa is the oldest and most prestigious liberal arts honor society in the country. The link above will take you to our webpage which has information about the history of the society, our selection procedures, and lists of students who qualified in recent years.

I am the Permanent Faculty Correspondent of our local chapter of Pi Mu Epsilon, the Alpha Omicron of New York, the National Mathematical Honor Society. For information about our newly formed chapter, follow the link above.

I had been a serious ice skater (figure skating, not hockey!) since 1968. I was a member of United States Figure Skating, and for a time I was a member of the Professional Skaters Association. From 1979 until 2022, I was a member of the Binghamton Figure Skating Club. For many years I served as President of the BFSC, sometimes as Vice-President or on the Board of Governors, and I have been a volunteer instructor in the Learn-to-Skate USA program run by the club. In March 2020 the SUNY Broome Ice Center, where the BFSC skated, was closed due to COVID, so I did not skate for about 18 months. Upon reopening of that rink, I tried to skate again, but found I had lost a lot of my stamina and balance. But I also found that my feet could not tolerate being in the boots for more than 40 minutes because of a nerve problem. That time grew shorter during September 2021, and on Oct. 9, 2021, I could only skate for 15 minutes, so I realized it was not worth trying anymore. I hoped that the problem would go away by itself, but apparently could only be treated by a nerve cutting surgery. Other issues had caused me to stop serving as BFSC president or officer, so in April 2022 I resigned my membership in the club. After 54 years of figure skating, I decided to just stop. The sport has been a huge part of my life, affording me great opportunities for personal growth, physical and mental challenges, and wonderful friendships. The link in the heading above this paragraph goes to a webpage where I have put my skating resume and some pictures.

Follow the indicated link to my Curriculum Vitae.

- Branching Rule Decomposition of the Level-1
E
_{8}^{(1)}-module with respect to the Irregular Subalgebra F_{4}^{(1)}⊕ G_{2}^{(1)}, A Ph.D. dissertation written by Joshua D. Carey under my direction. - A lightcone embedding of the twin building of a hyperbolic Kac-Moody group, A paper written in collaboration with Lisa Carbone (Rutgers University) and Walter Freyn. This manuscript was finally completed on June 13, 2019, revised after referee's comments, and accepted for publication in the SIGMA journal on May 9, 2020. The final version was uploaded to the arXiv on May 29, 2020. The precise reference and a link to the SIGMA website for this publication is: SIGMA 16 (2020), 045, 47 pages
- Decomposition of the rank 3 Kac-Moody Lie Algebra F With Respect to the rank 2 Hyperbolic Subalgebra Fib , A Ph.D. dissertation written by Diego Penta under my direction.
- Weyl Groups of Some Hyperbolic Kac-Moody Algebras, A paper written in collaboration with Daniel Vallières, Jan. 15, 2016, accepted for publication on May 5, 2017, in the Journal of Algebra, Special edition in honor of Efim Zelmanov. DOI: 10.1016/j.jalgebra.2017.05.003 The final citation for this paper is: Journal of Algebra 500 (2018), 457-497. A free download of the final version is available until April 10, 2018, from the following link: Feingold-Vallières JAlg500(2018). The proof of Theorem 6.5 in this paper refers to some calculations done with PARI. The PARI code used can be found at the following link: PARI code file and some explanation of the code can be found in the following text file: readme.txt file.
- Decomposition of Level-1 Representations of
D
_{4}^{(1)}With Respect to its Subalgebra G_{2}^{(1)}in the Spinor Construction , A Ph.D. dissertation written by Quincy Loney under my direction. - Branching Rule Decomposition of Irreducible Level-1
E
_{6}^{(1)}-modules with respect to F_{4}^{(1)}, A Ph.D. dissertation written by Christopher Mauriello under my direction. - The 3-State Potts Model and Rogers-Ramanujan Series, A paper written in collaboration with Antun Milas (SUNY-Albany), the Central European Journal of Mathematics, Jan. 2013, Vol. 11, Issue 1, pp. 1-16, (DOI) 10.2478/s11533-012-0086-7. A link to the online journal is here.
- Matrix Realizations of Hyperbolic Triangle Groups, A paper written in collaboration with Elizabeth Dwornik (Union-Endicott High School, Endicott, NY) as the culmination of a one-year mentoring project. This paper is looking for a home. If you know of a nice journal to which it should be submitted, please contact Alex Feingold.
- Hyperbolic Weyl Groups and the
Four Normed Division Algebras, A paper written in collaboration with Axel
Kleinschmidt (Universite Libre de Bruxelles & International Solvay Institutes,
Bruxelles, Belgium) and Hermann Nicolai (Max Planck Institute for Gravitational
Physics, Albert Einstein Institute, Golm, Germany),
Journal of Algebra 322 (2009), pp. 1295--1339. A Corrigendum (author's corrections) to
this paper is available through the following link:
Corrigendum to ``Hyperbolic Weyl Groups and the
Four Normed Division Algebras'' [J. Algebra 322 (2009) 1295-1339], J. Algebra 489 (2017), 586-587.
The arXiv copy of the 2009 paper has been updated to contain the corrections.
Another paper with the same title and authors as the 2009 paper
was published in the proceedings of an international
conference on vertex operators and related areas in honor of Geoffrey Mason. That
conference took place at Illinois State University in July, 2008. That shorter paper is an
introduction to and announcement of the results in this paper, and appeared in
**Vertex operator algebras and related areas**, Contemporary Mathematics, vol. 497, Amer. Math. Soc., Providence, RI (2009), 53-64. - A New Perspective on the Frenkel-Zhu Fusion Rule Theorem, A paper written in collaboration with Stefan Fredenhagen (Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Golm, Germany), submitted for publication in October 2007, accepted in June 2008, to appear in the Journal of Algebra 320 (2008), pp. 2079--2100.
- Fusion Algebras, Symmetric Polynomials, Orbits of N-Groups, and Rank-Level Duality, The Ph.D. thesis of Omar Saldarriaga, done under the direction of Alex Feingold. Also available as a pdf file: pdf file of Omar's thesis.
- Subalgebras of Hyperbolic Kac-Moody Algebras, Kac-Moody Lie Algebras and Related Topics, Ramanujan International Symposium on Kac-Moody Algebras and Applications, Jan. 28-31, 2002, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India, N. Sthanumoorthy, Kailash Misra, Editors, Contemporary Mathematics, Vol. 343, American Mathematical Society, Providence, RI, 2004, 97--114, (with Hermann Nicolai, Max Planck Institute for Gravitational Physics, Potsdam, Germany).
- Fusion Rules For Affine Kac-Moody Algebras, Kac-Moody Lie Algebras and Related Topics, Ramanujan International Symposium on Kac-Moody Algebras and Applications, Jan. 28-31, 2002, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India, N. Sthanumoorthy, Kailash Misra, Editors, Contemporary Mathematics, Vol. 343, American Mathematical Society, Providence, RI, 2004, 53--96.
- Valedictory Address by Alex J. Feingold to the Ramanujan International Symposium on Kac-Moody Lie Algebras and Applications, Jan. 28-31, 2002, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India.
- Type A Fusion Rules From Elementary Group Theory, Comtemporary Mathematics, Vol. 297, Proceedings of the Conference on Infinite-Dimensional Lie Theory and Conformal Field Theory, Editors: S. Berman, P. Fendley, Y. Huang, K. Misra, and B. Parshall, Charlottesville, VA, American Mathematical Society, Providence, RI, 2002 (with Michael Weiner), 97--115.
- Minimal Model Fusion Rules From 2-Groups, Letters in Mathematical Physics, Vol. 40, No. 2, April (II), 1997, 159-169, (with Fusun Akman and Michael D. Weiner).
- Spinor Construction of the c = 1/2 Minimal Model, Moonshine, The Monster, and Related Topics, Contemporary Mathematics, Vol. 193 (Chongying Dong and Geoffrey Mason, editors), American Mathematical Society, Providence, RI, 1995, pp. 45-92 (with John F. X. Ries and Michael D. Weiner).
- Constructions of vertex operator algebras, Proceedings of Symposia in Pure Mathematics, Vol. 56, Algebraic Groups and Their Generalizations, Editors William J. Haboush and Brian J. Parshall, American Mathematical Society, Providence, RI, April 1994, Part 2, 317-336.
- Representations of hyperbolic Kac-Moody algebras, Journal of Algebra, Vol. 156, No. 2, April 1993, 433-453 (with Igor B. Frenkel and John F. X. Ries).
- Spinor Construction of Vertex Operator Algebras, Triality and E_8^(1), Contemporary Mathematics, Vol. 121, American Mathematical Society, Providence, RI, 1991, 146 pp. monograph (with Igor B. Frenkel and John F. X. Ries).
- Classical Affine Algebras (1), Classical Affine Algebras (2), Classical Affine Algebras (3), Classical Affine Algebras (4), Classical Affine Algebras (5), Advances in Mathematics, Vol. 56, No. 2, May 1985, 117-172 (with Igor B. Frenkel). I divided the paper into five pdf files rather than one big file.
- Some applications of vertex operators to Kac-Moody algebras, Vertex Operators in Mathematics and Physics. Proceedings of a conference Nov. 10-17, 1983. Edited by J. Lepowsky, S. Mandelstam, I. M. Singer. Publications of the Mathematical Sciences Research Institute #3, Springer-Verlag, 1985, 185-206.
- A Hyperbolic Kac-Moody Algebra and the Theory of Siegel Modular Forms of Genus 2, Mathematische Annalen 263 (1983), 87--144, (with Igor B. Frenkel). Appearing here with the permission of Niedersachsische Staats-und Universitatsbibliothek, which has the volume at this link.
- MSRI Berkeley
- Public Broadcasting Service
- American Mathematical Society
- Max Planck Institut für Mathematik, Bonn, Germany
- Max Planck Institut für Gravitationsphysik, Albert Einstein Institute, Potsdam, Germany.
- Institut des Hautes Etudes Scientifiques.

## Interesting Mathematical Pictures From The Minnesota Geometry Center

- Picture 1, Jekyll and Hyde
- Picture 2, Red Eyes
- Picture 3, Crabs
- Picture 4, Frosted Pane
- Picture 5, Henon Ring
- Picture 6, Henon Isthmus
- Picture 7, Henon Crucified
- Picture 8, Hyperbolic Space Tiled with Dodecahedra
- Picture 9, Inversion
- Picture 10, Penrose by Quasitiler
- Picture 11, Escher Fish

## Pictures by Emily R. Feingold

## Judith M. Feingold's Art Website

## Caricatures of Alex Feingold

## 1974 Skit Written and Performed by Yale Classmates.

## Mathematical Parody Songs from the Skit by my Yale Classmates.

## Poetry written by Alex J. Feingold.

## Spin Art by Alex J. Feingold.

## Midi Music.

## Solomon Mandelkern History by Bernard Feingold.

Solomon Mandelkern was a famous biblical scholar, known for writing a concordance of the bible (Old Testiment). He is a distant relative of mine, and my father, Bernard Feingold, did a lot of research on Mandelkern's life and wrote a short biography which was published in an issue of the Jewish Historical Society of Maryland. A scaned copy of that article is available through the link above.

## Maryland Museum of Military History.

My father, Bernard Feingold, a retired Brig. General in the Maryland National Guard, was also very interested in military history, and helped to develop a museum at the Fifth Regiment Armory in Baltimore, Maryland. He served as a director of the museum, and started the collection of items of historical interest. The museum has considerably expanded since his passing in 1999.

This page was last modified on 1/17/2023.