Research Interests

(under constant development)


My research interest are divided into three main areas:

1.      Representations of affine Lie algebras, vertex theoretic structures and connections with integer partition theory;

1a. Mathematics related to Capparelli’s identities on partitions;

2.      Combinatorics of orthogonal polynomials and generalizations, integer sequences;

3.      Span of Hyperbolic Polynomials: algebraic integers and related topics.  

 

 

 

 

 

 

Some of my papers classified according to the above three areas:

Topic 1: a. Capparelli, Lepowsky, Milas, The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators, Ramanujan J. 12 (2006), no. 3, 379-397.

              b. Capparelli, On some theorems of Hirschhorn, Comm. Algebra 32 (2004), no 2, 629-635

              c. Capparelli, Lepowsky, Milas, The Rogers-Ramanujan recursion and intertwining operators, Commun. Contemp. Math. 5 (2003), no. 6, 947-966

              d. Capparelli, A construction of the level 3 modules for the affine Lie algebra A2(2) and a new combinatorial identity of the Rogers-Ramanujan type. Trans. Amer. Math. Soc. 348 (1996), no. 2, 481-501

              e. Capparelli, On some representations of twisted affine Lie algebras and combinatorial identities, J. Algebra 154 (1993), no. 2, 335-355   

 

Topic 2: a. Capparelli, Root power sums and Chebyshev polynomials, Rocky Mountain J. Math, 48 (2018), no. 1, 59-74

              b. Capparelli, Ferrari, Munarini, Zagaglia, A generalization of the “problem des rencontres”. J. Integer Seq. 21 (2018), no 2.

              c. Capparelli, Del Fra, Dyck paths, Motzkin paths, aand the binomial transform, J. Integer Seq. 18 (2015), no. 8

              d. Capparelli, Maroscia, On two sequences of orthogonal polynomials related to Jordan blocks, Mediterr. J. Math. 10 (2013), no. 4, 1609-1630.

              e. Capparelli, Del Fra, Pepe, Widened derangements and generalized Laguerre polynomials, Ramanujan J. to appear.

 

Topic 3: a. Capparelli, Del Fra, Chebyshev coordinates and Salem numbers, submitted

              b. Capparelli, Del Fra, Sciň, On the span of polynomials with integer coefficients, Math. Comp. 79 (2010), no. 270, 967-981.

 

 

Some papers related to the Capparelli identities:

 

1.      Capparelli, On some representations of twisted affine Lie algebras and combinatorial identities, J. Algebra 154 (1993), no. 2, 335-355

2.      Andrews, Schur’s theorem, Capparelli’s conjecture and q-trinomial coefficients, Contemp. Math., 166, Amer. Math. Soc. 1994.

3.      Capparelli, A combinatorial proof of a partition identity related to the level 3 representations of a twisted affine Lie algebra, Comm. Algebra 23 (1995) no. 8, 2959-2969

4.      Alladi, Andrews, Gordon, Refinements and generalizations of Capparelli’s conjecture on partitions, J. Algebra 174 (1995), no. 2, 636-658

5.      Capparelli, A construction of the level 3 modules for the affine Lie algebra A2(2) and a new combinatorial identity of the Rogers-Ramanujan type. Trans. Amer. Math. Soc. 348 (1996), no. 2, 481-501

6.      Sills, On series exapansions of Capparelli’s infinite product. Adv. in Appl. Math. 33 (2004), no. 2, 397-408

7.      Alladi, Remembering Basil Gordon, Notices AMS, August 2013.

8.      Bringmann, Mahlburg False theta functions and companions to Capparelli’s identities. Adv. Math. 278 (2015) 121-136

9.      Berkovich, Uncu A new companion to Capparelli’s identities, Adv. in Appl. Math. 71 (2015), 125-137

10.  Bringmann, Mahlburg Three-colored partitions and dilated companions of Capparelli’s identities, Analytic number theory, modula forms and q-hypergeometric series, 139-156, Springer Proc. Math. Stat., 221, 2017

11.  Fu, Shishuo, Zeng Jiang A unifying combinatorial approach to refined little Göllnitz and Capparelli’s companion identities. Adv. in Appl. Math. 98 (2018), 127-154

12.  Dousse, Lovejoy, Generalizations of Capparelli’s identity, arXiv preprint, arxiv:1702.07249, 2017

13.  Kursungoz, Andrews-Gordon type series for Capparelli’s and Göllnitz-Gordon identities, arXiv:1807.11189, 2018

14.  Alladi, My association and collaboration with George Andrews,

15.  Alladi, Andrews, Ono, McIntosh, On the work of Basil Gordon, Journal of Combinatorial Theory, Series A, 113 (2006) 21-38

16.  Kanade, Some results on the representation theory of vertex operator algebras and integer partition theory, 2015

17.  Kanade, Russell, Staircases to analytic sum-side for many new integer partition identities of Rogers-Ramanujan type, arXiv:1803.032515, 2018

18.  Nandi, Partition identities arising from the standard A2(2)-modules of level 4,

19.  Berkovich, Uncu, Polynomial identities implying Capparelli’s partition theorems, arXiv 1807.10974

20.  Dousse, The method of weighted words revisited, arXiv:1702.07177

21.  Primc,Sikic: Leading terms of relations for standard modules of affine Lie algebras Cn(1) arXiv:1506.05026

22.  Bringmann et al. Proofs and reductions of Kanade Russell’s partition identities, arXiv:1809.06089

23.  Sills, A classical q-hypergeometric approach to the A2(2) standard modules, AlladiFest, Florida 2016

24.  Berkovich, Uncu, Elementary polynomial identities involving q-trinomial coefficients, arXiv 1810.06497v1, 2018

25.  Berkovich, Uncu, Refined q-trinomial coefficients and two infinite hierarchies of q-series identities, arXiv: 1810.12048

26.  Dousse, On partition identities of Capparelli and Primc, arXiv:1811.02251

27.  Kanade, Searching for modular companions, arXiv:1902.05199

 

 

Photos/Memories

 

 

 

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Taken by A. Sills during a visit to the Rutgers Math Department, New Jersey, USA, on 9 April 2004. From left to right: Freeman Dyson (cf. also here), S. C., Jim Lepowsky, George Andrews (cf. also here)

 

University of Florida at Gainesville 2004

 

(Photo Courtesy of K. Alladi: thanks!)

Standing, left to right: S.C., G. Andrews, K. Alladi.

Seating, left to right: J. Lepowsky, B. Gordon.

See  August 2013 issue of the "Notices of the American Mathematical Society" ,in particular: Remembering Basil Gordon

 

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Con Peter Lax, 28 giugno 2007

 

 

Convegni Vari:

 

Napoli 2018

 

Combinatorics, Arco di Trento 2018

 

Vertex algebras and related topics

Zagreb, May 24-27, 2018

A workshop in honor of Mirko Primc on his 70th birthday

Schedule

Abstracts

 

 

Discretaly

A workshop in Discrete Mathematics

Rome, February 1-2, 2018

Program and Abstracts

Group Photo

 

Catania 2017

 

Milano 2017

 

 

 

Pagina del Gruppo di Geometria

 

Maratea 2016

 

XX Congresso Unione Matematica Italiana Siena 2015

 

Gaeta 2014: foto

 

Cetraro 2013

 

Parigi 2013

http://www.liafa.jussieu.fr/fpsac13/?sec=program

 

Combinatorics 2012

 

Conference in Honor of Jim Lepowsky and Robert Wilson

 

Workshop2004: Workshop "Automorphic Representations and Related Topics"
Erwin Schrödinger Institute, Vienna,
December 06-09, 2004

 

University of Florida conference

 

Dubrovnik Conference

 

Primo Incontro Italiano di Teoria dei numeri

 

AMS Meeting