Mathematics and Computer Science
Office Location: AC-2C07B
|PhD||University of Illinois||Mathematics||2006|
|BA||University of Chicago||Mathematics||1996|
Areas of Expertise
- Algebraic Combinatorics
Representations of Finite Groups
Books in Field Of Expertise
R. Nath, S. Garfunkel (Co-editors). Geometry, Games, Graphs and Education. Boston: COMAP, Inc., November 8th, 2008. .
Articles in Field Of Expertise
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.
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).
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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.
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.