Nath, Rishi

Professor

Mathematics and Computer Science

Phone: 718-262-2535
Office Location: AC-2C07B
Email: rnath@york.cuny.edu

Dr. Nath first became interested in mathematics at the University of Chicago where he attended various courses on group theory and Lie algebras given by Professors Jon Alperin and George Glauberman. After completing a Masters degree at Brandeis University, he returned to Chicago where he completed his PhD in the representation theory of the symmetric and alternating groups under the direction of Professor Paul Fong at the University of Illinois. Dr. Nath has a longstanding interest in math education. He taught math at Bronzeville Alternative High School in the South Side of Chicago and with the Franklin Summer Program (Phillips Brooks House, Harvard University). Originally from the Boston area, he currently lives in Queens.

Office Hours

Day	Time

Tuesday	3:00-4:00pm
Thursday	3:00-4:00pm

Education

Degree	Institution	Field	Dates
PhD	University of Illinois	Mathematics	2006
MA	Brandeis University	Mathematics	1999
BA	University of Chicago	Mathematics	1996

Areas of Expertise

Algebraic Combinatorics
Representations of Finite Groups
Partition Theory

Publications in Field Of Expertise

Books

R. Nath, S. Garfunkel (Co-editors). Geometry, Games, Graphs and Education. Boston: COMAP, Inc., November 8th, 2008. .

Articles

R. Nath with O. Brunat. "Core and quotients through Frobenius symbols." . : .

R. Nath with O. Brunat. "A crank-based approach to theory of 3-core partitions." Proceedings of the American Mathematical Society. just accepted: .

R. Nath with O. Brunat. "The Navarro Conjecture for the Alternating Groups." Algebra & Number Theory. forthcoming 2021: .

R. Nath with J.B. Gramain and J.A. Sellers. "Simultaneous core partitions with nontrivial common divisor." The Ramanujan Journal. forthcoming 2020: .

R. Nath. "Advances in the theory of cores and simultaneous core partitions.." Amer. Math. Monthly. 124 2017: 844-861.

R. Nath. "Abaci structures of (s,ms±1)-core partitions." Electron. J. Combin.. 24 2017: 1-20.

R. Nath with J.A. Sellers. "Congruences for the number of spin characters of the double covers of the symmetric and alternating groups." Adv. in Appl. Math.. 80 2016: 114-130.

R. Nath. "A combinatorial proof of a relationship between maximal (2k−1,2k+1)-cores and (2k−1,2k,2k+1)-cores.." Electron. J. Combin.. 23 2016: 1-13.

R. Nath. "Symmetry in maximal (s−1,s+1) cores." Integers Integers: Electronic Journal of Combinatorial Number Theory. A18 2016: 1-23.

R. Nath with C. Hanusa. "The number of self-conjugate partitions." Journal of Number Theory. 133, no. 2 2013: 751-768.

R. Nath with J.B. Gramain. "On core and bar-core partitions." The Ramanujan Journal. 27, no. 2 2012: 229-233.

R. Nath with W. Keith. "Partitions with prescribed hooksets." Journal of Combinatorics and Number Theory. 3, no. 1 2011: 39-50.

R. Nath. "On the Navarro conjecture for the A(n), p=2." Journal of Algebra and its Applications. 8, Issue 6 December 2009: 837-844.

R. Nath. "The Isaacs-Navarro conjecture for the alternating groups." Journal of Algebra. 321, Issue 6 March 15, 2009: 1632-1642.

R. Nath. "On the s-core of a t-core partition." Integers: Electronic Journal of Combinatorial Number Theory. A28 June 16, 2008: 1-5.

Other

Presented Papers, Lectures, and Exhibitions and Performances

"Simultaneous core partitions with nontrivial common divisor" May 23, 2019: CANT 2019, Graduate Center CUNY.

"Enumerating simultaneous core partitions" October 8, 2016: Integers Conference 2016, University of West Georgia.

"Sequences of simultaneous core partitions" May 27th, 2016: CANT 2016, Graduate Center, CUNY.

"Recent results using self-conjugate partitions" June 19, 2014: Seminaire Claude Chevalley, University of Paris.

"A simultaneous core partition walks into a bar" May 20th, 2015: Combinatorics Seminar, Massachusetts Institute of Technology.

"Results on simultaneous core partitions" Nov 18, 2014: Partition Seminar, Penn State University.

"Conjectures and results on self-conjugate partitions" October 25, 2013: Integers Conference, University of West Georgia.

"Ten facts about self-conjugate partitions" May 23rd, 2013: CANT 2013, Graduate Center CUNY.

"The Durfee Square and the quotient of a self-conjugate partition" May 24, 2012: CANT 2012, Graduate Center CUNY.

"Simultaneous core partitions" October 24, 2011: Integers Conference, University of West Georgia.

"Refinements of the McKay conjecture in the case of the symmetric and alternating groups" April 23rd, 2010: Representation Theory Seminar, CUNY Graduate Center (invited).

"Combinatorics and the Navarro-Willems conjecture" November 19th, 2010: Algebra Seminar, CUNY Graduate Seminar (invited).

"Combinatorics arising from the Navarro-Willems conjecture" October 2nd, 2010: Special Session on Lie Algebras and Representation Theory, American Mathematical Society (AMS) Fall Eastern Sectional Meeting, Syracuse University (invited).

"Recovering diagonal hooks of self-conjugate partitions" July 2nd, 2010: Algebra Seminar, University of Copenhagen (invited).

"Welter's game and Young diagrams" May 26th, 2010: CANT 2010, CUNY Graduate Center (invited).

"On hook-lengths of self-conjugate partitions" November 4th, 2009: Combinatorics Seminar, Massachusetts Institute of Technology (MIT) (invited)..

"p-core partitions and the symmetric group: Recent Results" October 15th, 2009: Integers Conference, University of West Georgia (invited)..

"Some properties of 3-cores" May 27th, 2009: CANT 2009, CUNY Graduate Center.

"On diagonal hooks of symmetric partitions" December 7th, 2008: Combinatory Analysis 2008, Penn State University (invited).

"Results on p-cores using the abacus" May 22nd, 2008: CANT 2008, CUNY Graduate Center (invited).

"Recent results on partitions and hooks using the abacus" October 29, 2008: Department of Mathematical Sciences Seminar, Montclair State University, Montclair, New Jersey (invited)..

"Recent developments in Algebra" January 28th, 2008: Department Seminar, University of the West Indies (UWI)-St. Augustine, Trinidad and Tobago (invited).

"Recent Refinements of the Mckay conjecture" January 30th, 2007: Society of Mathematicians Seminar, Stevens Institute of Technology (invited).

Professional Honors, Prizes, Fellowships

York College Presidents Excellence in Research Award: September 2018.

Visitor, Mathematical Science Research Institute, Berkeley, CA: April 8- April 13, 2018.

Visitor, Global/Local Conjectures in Representation Theory of Finite Groups, Banff International Research Station: March 16th-March 23rd, 2014.

Outstanding Student Advocate Award, CUNY Honors Opportunities Conference: March 2012.

Visitor, Ecole Polytechnic Federale Lausanne (EPFL), Jacques Thevenaz Conference, http://grt.epfl.ch/: June 22nd - June 25th, 2010.

Visitor, Homological Methods in Representation Theory, Mathematical Sciences Research Institute (MSRI): March 31st - April 4th, 2008.

Grants-In-Aid

TRADA-50-645, Simultaneous core partitions and lattice paths. July 1st, 2019 - June 31st, 2020: $3,276.00.

TRADA-49-300, The Navarro conjecture for the double covers of.... July 1st, 2018 - June 31st, 2019: $3,489.20.

TRADA-47-785, Wreath products, core towers, and the Navarro c.... July 1st, 2016 - June 31st, 2017: $3,490.00.

TRADA-46-493, Arithmetic congruences for simultaneous core pa.... July 1st, 2015 - June 31st, 2016: $3,465.00.

PSC_CUNY TRAD 44-576, Self-Conjugate Partitions: New and Existing Results. July 1st, 2013 - June 31st, 2014: $2933.00.

PSC-CUNY TRAD 43-449, Self Conjugate partitions and the representation theory. July 1st, 2012 - June 31st, 2013: $1300.00.

PSC-CUNY TRAD 42-615, Recent results on simultaneous core partitions. July 1st, 2011 - June 31st, 2012: $3428.00.

PSC-CUNY REG-41, Refinements of the McKay conjecture for the covering groups of the symmetric and alternating groups (PI). July 1st, 2010 - June 31st, 2011: $3325.00.

PSC-CUNY REG-40, A conjecture of Turull in the alternating groups (PI). July 1st, 2009 - June 31st, 2010: $2660.00.

PSC-CUNY REG-39, Navarro's conjecture for the alternating groups (PI). July 1st, 2008 - June 31st, 2008: $3525.00.

Mathematics Association of America (MAA), Tensor Scholars (Co-PI with Dr. Lidia Gonzalez). September 1st, 2010 - August 31st, 2011: $6000.00.

Mathematics Association of America (MAA), Tensor Scholars (Co-PI with Dr. Lidia Gonzalez). September 1st, 2009 - August 31st, 2010: $6000.00.

Title III--Center for Teaching and Learning (CETL), York College, Shifting the Center (PI). September 1st, 2009 - August 31st, 2010: $3000.00.

Other Professional Activities and Public Service

Referee, Ramanujan Journal: 2018.

Referee, Integers: The Electronic Journal of Combinatorial Number Theory: 2018.

Referee, Acta Arithmetica: 2018.

Referee, Science China Mathematics: 2018.

Referee, Discrete Mathematics: 2017.

Referee, Discrete Mathematics: 2015.