Contact Information:
Algebra and Number Theory Seminar 2005-2006 2006-2007 ,
2007-2008 ,
2008-2009 ,
2009-2010 ,
2010-2011 ,
2011-2012 ,
2012-2013 2013-2014 2014-2015 ,
2015-2016 ,
2016-2017 ,
2017-2018 ,
2018-2019 q KIM Team:Kevin Allen (PhD student)Björn Johannesson (PhD student)Matthias
Storzer (Postdoc)Yuma
Mizuno (Postdoc)Matthew
Litman (Assistant Professor) Asymptotic
counting and L-functions , MPIM, May 5-9, 2025The
SEA seminar , University of Galway, May 19, 2025Modular
forms in String Theory , BIRS, Banff, September 25-30, 2016Hypergeometric
motives and Calabi-Yau differential equations , MATRIX
Institute, Creswick, January 8-27, 2017Low-dimensional topology
and number theory , MFO, August 20-26, 2017Trends in
Modular Forms , NIMS, Daejeon, December 19-22, 2017Periods in Number Theory, Algebraic
Geometry and Physics , HIM, Bonn, January 3-19, 2018Modular
forms and quantum knot invariants , BIRS, Banff, March 11-16,
2018AMS
Special Session on Mock modular and quantum modular forms ,
Portland State, April 14-15, 2018Antalya Algebra
Days XX , Nesin Mathematics Village, May 16-20, 2018Number
Theory and Algebra Seminar , University of Zagreb, October 30,
2018Modularity and
3-manifolds , ICERM, March 8-10, 2019MPIM Number Theory
Seminar , March 13, 2019Algebra
Seminar , TU Darmstadt, April 23, 2019James M. Flaherty
Visiting Professor , McMaster University, May 17-August 9, 20192nd q -Day:
q -series and related topics, KIAS, August 16, 2019 Fields
Institute Undergraduate Summer Research Program , July 2-August
30, 2019Colloquium
and Flaherty Public Lecture , McMaster University, September
27, 2019Vanderbilt Number
Theory Seminar , November 17, 2020Warsaw
Number Theory Seminar , November 30, 2020EIMI Number Theory
Seminar , December 8, 2020
SFB F50 Statusseminar , December 14-16, 2020Modularity in
Quantum Systems , KITP, November 30-December 18, 2020Graduate
Colloquium , University of Denver, April 23, 2021New connections in
number theory and physics , Isaac Newton Institute, Cambridge,
May 24-28, 2021Number Theory, Strings
and Quantum Physics , Kavli IPMU, May 31-June 5, 2021watch the
student talks!)MFO, Research in
Pairs , January 9-22, 2022MPIM Number Theory
Seminar , March 30, 2022AMS
Special Session on q -series, number theory and quantum
topology , co-organizer, University of Denver, May 14-15, 2022
Okinawa Institute of Science and
Technology , June 9 - September 1, 2022Kyushu
Mathematical Physics Seminar , Fukuoka, July 20, 2022slides and
thesis ,
September 5, 2022Representation
Theory XVII , Dubrovnik, October 3-8, 2022IRIF , Paris, December 4-17,
2022IRIF , Paris, July 2-8, 2023UCD
Undergraduate Research Projects , Summer 2023 (come watch the
student talks!)Exact
Asymptotics: From Fluid Dynamics to Quantum Geometry , OIST ,
Okinawa, August 28-September 15, 2023 Mathematical
Sciences Seminar Series , UCC, November 29, 2023University of Geneva ,
December 13-17, 2023Colloquium
talk , NISER , Bhubaneswar, January
5-12, 2024School
of Mathematical and Statistical Sciences Seminar , University
of Galway, January 30, 2024The
Web of Modularity , Tulane University, February 22-25, 2024Arbeitsgemeinschaft
Diskrete Mathematik , University of Vienna, May 28, 2024UCD
Undergraduate Research Projects , Summer 2024 (come watch the
student talks!)New
developments in representation theory of algebras , OIST ,
Okinawa, November 18-30, 2024 cv student
comments UCD profile UCD Today article, Spring 2020 (see page 15)UCD
College of Science Research and Teaching Showcase UCD
Today article, Spring/Summer 2023 (see page 34) OIST
Theoretical Sciences Visiting Program Public Talk , Okinawa,
July 7, 2022IRC
Advanced Laureate Award , 2023-2027ICUF
article LSU
article Journal
of Combinatorial Theory, Series A Canadian
Journal of Mathematics Canadian
Mathematical Bulletin Canadian
Mathematical Communications Unimodal
sequences and mixed false theta functions ",Advances in Mathematics , accepted for publication.Resurgence,
Habiro elements and strange identities ",Communications in Number Theory and Physics , accepted for
publication.Knot theory and Rogers-Ramanujan type
identities ", Srinivasa Ramanujan: His Life,
Legacy and Mathematical Influence (Springer) , accepted for
publication.On sporadic sequences ",Monatshefte für Mathematik , 205, no. 2, (2024), 217-234.Rank
deviations for overpartitions ",Research in Number Theory , 10, no. 3, (2024), Paper No. 67.Asymptotics and
sign patterns for coefficients in expansions of Habiro elements ",Mathematische Zeitschrift, 304, no. 4, (2023), 57.A q -multisum
identity arising from finite chain ring probabilities ",Electronic Journal of Combinatorics , 29, no. 2, (2022), Paper
No. 2.4.The
colored Jones polynomial and Kontsevich-Zagier series for double
twist knots ",Journal of Knot Theory and its
Ramifications , 30, no. 5, (2021), 2150031.Quantum
modularity of partial theta series with periodic coefficients ", Forum Mathematicum , 33,
no. 2, (2021), 451-463.Variations of
Andrews-Beck type congruences ", Journal of Mathematical Analysis
and Applications , 495, no. 2, (2021), 124771.Generalized
Fishburn numbers and torus knots ", Journal of Combinatorial Theory,
Series A , 178 (2021), 105355.FUSRP
final report )Sequences,
modular forms and cellular integrals ", Mathematical Proceedings of the
Cambridge Philosophical Society , 168, no. 2, (2020),
379-404.The
colored Jones polynomial and Kontsevich-Zagier series for double
twist knots, II ", New York Journal of Mathematics ,
25 (2019), 1312-1349.Interpolated
sequences and critical L-values of modular forms ", , 327-349, Texts & Monographs in
Symbolic Computation, Springer, 2019.Constrained
ternary
integers ", International Journal of Number
Theory , 15, no. 2, (2019), 407-431.A modular
supercongruence for 6 F5 : an Apéry-like
story ",Annales de l'Institut Fourier
(Grenoble), 68, no. 5, (2018), 1987-2004.Mock
theta double sums ", Glasgow Mathematical Journal ,
59, no. 2, (2017), 323-348.q -series and tails of colored
Jones polynomials Indagationes Mathematicae, 28,
no. 1, (2017), 247-260.On a
conjecture of Kimoto and Wakayama ", Proceedings of the American
Mathematical Society , 144, no. 10, (2016), 4319-4327.The first
positive rank and crank moments for overpartitions ", Annals of Combinatorics ,
20, no. 2, (2016), 193-207.Supercongruences
for
sporadic sequences ", Proceedings of the Edinburgh
Mathematical Society (2), 59, no. 2, (2016), 503-518.Rogers-Ramanujan
type identities for alternating knots ", Journal of Number Theory ,
161, (2016), 255-280.On the
(K.2) supercongruence of Van Hamme ", Journal of Mathematical Analysis
and Applications , 433, no. 1, (2016), 706-711.On recursions for
coefficients of mock theta functions ", Research in Number Theory ,
1:29 (2015). Real
quadratic double sums ", Indagationes Mathematicae ,
26, no. 4, (2015), 697-712.On two 10th
order mock theta identities ",The Ramanujan Journal , 36,
no. 1-2, (2015), 117-121., "q -hypergeometric
series,
alternating knots and identities ", Oberwolfach Reports , 11,
no. 3, (2014), 2164-2167.Mixed mock
modular q -series ", Journal of the Indian
Mathematical Society, New Series. Special volume to
commemorate the 125th birth anniversary of Srinivasa Ramanujan,
(2013), 45-61.q -hypergeometric double sums
as mock theta functionsPacific Journal of Mathematics ,
264, no. 1, (2013), 151-162.A
supercongruence for generalized Domb numbers ",Functiones et Approximatio
Commentarii Mathematici , 48, no. 1, (2013), 29-36.The Bailey
chain and mock theta functions ", Advances in Mathematics ,
238 (2013), 442-458.Principal forms X^2
+ nY^2 representing many integers ",Abhandlungen aus dem
Mathematischen Seminar der Universität Hamburg , 81, no. 2,
(2011), 129-139.Supercongruences for
Apéry-like numbers ", Advances in Applied Mathematics ,
47, no. 3, (2011), 631-638.Congruences via
modular forms ",Proceedings of the American
Mathematical Society, 139, no. 7, (2011), 2375-2381. Quadratic forms
and four partition functions modulo 3 ",Integers , 11, no. 1,
(2011), 47-53. Supercongruences
satisfied by coefficients of 2 F1
hypergeometric series ",Annales des sciences mathématiques
du Québec , 34, no. 1, (2010), 25-36.M2 -rank
differences
for overpartitions ",Acta Arithmetica, 144, no.
2, (2010), 193-212.Automorphic
properties of generating functions for generalized rank moments
and Durfee symbols ",International Mathematics Research
Notices , no. 2, (2010), 238-260."Rank and
crank moments for overpartitions" , Journal of Number Theory ,
129, (2009), 1758-1772."M2 -rank
differences
for partitions without repeated odd parts" , Journal de Théorie des Nombres de
Bordeaux , 21, no. 2, (2009), 313-334."Gaussian
hypergeometric series and supercongruences" ,Mathematics of Computation, 78, no. 265, (2009), 275-292. A p -adic
analogue of a formula of Ramanujan ",Archiv der Mathematik , 91,
no. 6, (2008), 492-504."Rank
differences for overpartitions" ,The Quarterly Journal of
Mathematics , 59, no. 2, (2008), 257-273."Congruences for
traces of singular moduli" , The Ramanujan Journal , 14,
no. 3, (2007), 411-419."Representations
of
integers by certain positive definite binary quadratic forms", The Ramanujan Journal , 14,
no. 3, (2007), 351-359."On a conjecture of
Wilf" ,Journal of Combinatorial Theory,
Series A, 114, no. 7, (2007), 1332-1349."Two-dimensional
lattices with few distances" ,L'Enseignement Mathématique ,
52, (2006), 361-380."On sums of
three squares" , International Journal of Number
Theory , 1, no. 2, (2005), 161-173."A remark on a
conjecture of Borwein and Choi" , Proceedings of the American
Mathematical Society , 133, no. 10, (2005), 2903-2909."Vanishing
of
eigenspaces and cyclotomic fields" ,International Mathematics Research
Notices , no. 20, (2005), 1195-1202."A note on
4-rank densities" , Canadian Mathematical Bulletin ,
47, (2004), 431-438."Tame kernels and
further 4-rank densities" ,Journal of Number Theory ,
98, (2003), 390-406."Densities of
4-ranks of K_2(O)" , Acta Arithmetica, 102,
(2002), 45-54.Densities
of 4-ranks of K_2 of rings of integers ",Undergraduate Students: Fields
Institute Undergraduate Summer Research Program , July 1-August
29, 2019MSc Students: Somos
sequences and cluster algebras PhD Students: 5. Björn Johannesson, PhD, starting
9/2024Kevin Allen , PhD
student, 9/2021 to current, UCDPaul Beirne ,
PhD 2020, UCD IRC Postgraduate Scholarship 2. Dermot McCarthy ,
PhD 2010, UCDp -adic hypergeometric series and
supercongruences 1. Stefan de Wannemacker, PhD 2006,
UCD Postdoctoral
Fellows: 5.
Matthias
Storzer , October 2024-September 2027, UCD Advanced Laureate
Award Postdoc Yuma Mizuno , April
2024-March 2027, UCD2. Brundaban
Sahu , Nov. 2008-Oct. 2010, UCD AMS
Special Session on q -series, number theory and quantum
topology , University of Denver, May 14-15, 2022 Workshop on
Enumerative Combinatorics , UCD, March 10, 2021Modular
forms and quantum knot invariants , BIRS, Banff, March 11-16,
2018
Workshop on vertex operator algebras and mock modular forms ,
NUI Galway, May 22-23, 201527th
Automorphic
Forms Workshop , UCD, March 11-14, 2013Algebraic K-theory and
Arithmetic , Banach Center, Bedlewo, Poland, July 22-28,
2012Prospects in q -series and modular
forms , UCD, July 14-16, 2010AMS
Special
Session on Number Theory and applications in other fields ,
LSU, March 28-30, 2008AMS
Special
Session on Algebraic Number Theory and K-theory , LSU,
March 14-16, 2003Grants: IRC Advanced Laureate Award, December 2023 -
November 2027q KIM: q -series, quantum knot invariants and
modularity" € 993,160 € 16,000 € 1800 q KI+TQC" €21,800 € € 1500 UCD Seed Funding Scheme, February 2016q -series and quantum
knot invariants" € 1100 € 6000 Number Theory Foundation, January 2010q -series
and modular forms" Math Links: UCD School of Mathematics and
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