Dr. Ashish Kumar Upadhyay

Research Areas:Combinatorial Topology and Geometry, Geometric Topology, Algebraic Topology, Algorithmic and Combinatorial aspects of Low - dimensional Manifolds, Graphs on Surfaces, Automorphism Groups, Coding theory over rings, Spectra of Graphs and SurfacesStudents:Ph.D: 02 Completed, 06 Ongoing, M.Tech. & MSc : 09 Completed, 03 OngoingCourses taught at IITP :Calculus, Linear Algebra, ODE, PDE, Computational Topology, Graphs Groups and Networks, Discrete Mathematics, Calculus on Manifolds, Algebraic Topology, Measure Theory, Algebra, Topology, Graph Theory, Differential Geometry(IITP)

Sponsored Projects:Two DST projects completed.Publications:

• Basudeb Datta and Ashish Kumar Upadhyay, Degree Regular triangulations of the torus and Klein bottle, Proc. Indian Acad. Sc. (Math Sc.) vol 115, No. 3, August 2005, pp- 279 - 307.
• Basudeb Datta and Ashish Kumar Upadhyay, Degree regular triangulations of the double torus, Forum Mathematicum, vol 18, issue 6, November 2006, pp-1011-1026.
• Ashish Kumar Upadhyay, Erratum-On Degree regular triangulations of torus and Klein bottle, Proc. Indian Acad. Sciences (Math. Sc.) vol 118, No. 2, May 2008, pp - 320.
• Ashish Kumar Upadhyay, On an Equivalence of Simplicial Polytopes, Int. J. Contemp. Math. Sciences, vol 4, 2009, no. 30, 1473 – 1478
• Ashish Kumar Upadhyay, A note on upper bound for d-covered triangulation of closed surfaces, Int. JPAMS, 67(1), 1-5, 2011
• Ashish Kumar Upadhyay, Contractible Hamiltonian Cycles in Triangulated Surfaces, Elemente der Mathematik,  69(1),  23–29, 2014
• Frank H. Lutz, Thom Sulanke, Anand K. Tiwari, Ashish K. Upadhyay, Equivelar and d- Covered Triangulations of Surfaces – I, Graphs and Combinatorics (accepted),
• Dipendu Maity and Ashish K. Upadhyay, Contractible Hamiltonian Cycles in Polyhedral Maps, Discrete Math. Algorithms and Applications 04, 4 (2012) 10 pp.
• Ashish K. Upadhyay, Anand K. Tiwari and Dipendu Maity, Semi Equivelar Maps, Beitrage zur Algebra und Geometrie , 55(1), 229-242, 2014
• Anand K. Tiwari and Ashish K. Upadhyay,  Semi equivelar maps on the torus and the   Klein bottle with few vertices, Math. Slovaca , 67(2), pp. 519-532, 2017
• Dipendu Maity and Ashish K. Upadhyay,  A note on edge-disjoint contractible 
• Hamiltonian cycles in polyhedral maps, Electronic J. Graph Th. App. 2 (2), 160-165, 2014
• D Maity and Ashish K Upadhyay,  Hamiltonian cycles in polyhedral map, Proc. Indian Acad Sc.(Math. Sc.),  127 (2017) 737 – 751
• Anand K Tiwari and Ashish Kumar Upadhyay, Semi-equivelar maps on the surface of Euler characteristic $-1$, Note Mat. 37 (2017) no. 2, 91-102
• Ashish Kumar Upadhyay and D Maity,  On the enumeration of a class of toroidal graphs, Contributions to Discrete Mathematics, 13 (2018) 79 – 119
• D Maity and Ashish Kumar Upadhyay,  Some Centrally Symmetric Manifolds, Journal of the Ramanujan Mathematical Society , 2019, (to appear)
• D Maity and Ashish Kumar Upadhyay,  Corrigendum to ``On the enumeration of a class of toroidal graphs, Contributions to Discrete Mathematics (to appear)
• T Bag, M Ashraf, G Mohmmad and A K Upadhyay, Quantum codes from cyclic codes over the ring Fp[u]/ < u3 − u >, Asian-European Journal of Mathematics, June 2018
• T Bag, H Islam, O Prakash and A K Upadhyay,  A study of constacyclic codes over the ring ℤ4[u]/<u2 - 3>, Discrete Mathematics Algorithms and Applications, June 2018
• T Bag and Ashish Kumar Upadhyay, Skew cyclic and skew constacyclic codes over the ring Fp + u1Fp + ⋯ + u2mFp,  Asian-European Journal of Mathematics, June 2018.
• T Bag and Ashish Kumar Upadhyay, Study on negacyclic codes over the ring $$\mathbb {Z}_{p}[u]/, Journal of Applied Mathematics and Computing, June 2018
• Ashish Kumar Upadhyay , R Islam, and S Maity,  Corrigendum to “The multiplicative Zagreb co-indices on two graph operators” Bul. Acad. Ştiinţe Repub. Mold. Mat., 2016, no. 2(81), 18–26”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 2, 138–140
• T Bag, A Dertli, Y Cengellenmis and A K Upadhyay, Application of Constacyclic Codes over the Semi Local Ring $F_{p^m}+vF_{p^m}$ , Indian J PAM, (to appear)
• T. Bag, Sachin Pathak and A K Upadhyay, (2019) Classes of constacyclic codes of length p^s over the ring Fpm + uFpm + vFpm + uvFpm, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. (to appear)
• Dipendu Maity and A K Upadhyay, (2019), Hamiltonicity of a class of toroidal graphs, Math Slovaca (to appear)

Talks:

• Proper Trees and Contractible Hamiltonian Cycles in Combinatorial 2- Manifolds, International Conference on Cycles in Graphs (in conjunction with the 27th Annual Shanks Lecture) May 30 - June 2, 2012, Vanderbilt University, Nashville, Tennessee, USA
• On d-Covered triangulations of Closed Surfaces, AMS – 2012, October 5 – 7, 2012, MNNIT, Allahabad.
• On d-Covered triangulations of Closed Surfaces, RAMA – 2013, Feb 14 – 16, 2013, ISM, Dhanbad.
• Six lectures on Fundamental group and Covering Spaces,  ATM School for lecturers,  December 2013, HRI, Allahabad.
• Semi-equivelar maps on surfaces, 1 hr  invited talk  delivered during annual conference of Indian Math Society, 27 – 30 December 2014 ISM Dhanbad.
• On some results in Semi – equivelar Maps, invited talk delivered in Department of Mathematics Veer Kunwar Singh University Ara, 25 May 2015, Ara.
• Invited talk in Delhi University on occasion of 60^th Birthday of Prof Tej Bahadur Singh, 2017.
• Invited Talk in the Conference of Mathematical Society of BHU on Combinatorics in BHU, Feb 2019.
• Plenary Lecture – On PL Structures: Work of Prof B L Sharma, in B N College Patna, 15 March 2019.
• The God's Number !!, in Workshop on Science, Imagination and Discovery organized by CEERI and BITS -Pilani during 14 to 22 May 2007.
• On some enumeration results and techniques in Combinatorial Topology, Departmental Seminar, Indian Institute of Technology, Kanpur,  August 27th, 2007.
• Classification of a class of combinatorial 2-manifolds, Seminar at Indian Institute of Science Education and Research, Pune,  October 12, 2007.
• Some observations in Mathematics, Model lecture in Mathematicsfor School teachers and administrators, Birla Institute of Technology and Science, Pilani - October 28th, 2007.

Workshop/Conferences
:

• “Science Academies’ Lecture workshop on PDEs”, March 3-5, 2011, IIT Patna (localconvener with Prof. Phoolan Prasad as convener)
• “Basic training program in Mathematics for undergraduate students”, May 10 – 20,2011, IIT Patna, (Convener)
• "ATML", May 1 to 13, 2017 (convener)
• ATML, 2017
• NASI TIMC Workshop on Coxeter Group, 2018
• Annual Meeting of Math Soc of BHU, 2019
• National Conference, B N College, 2019

Administrative responsibilities
:Coordinator of the Dept. of Mathematics, IIT Patna , Member of Senate of IIT Patna, Member of the Institute academic program committee, Faculty in-charge of institute website, Faculty in-charge of institute Seminar , Chairman of the disciplinary committee, IIT Patna, Associate faculty for TEQIP-MHRD and ranking of the institute, Coordinator and Convener Institute academic program committee, Chairman, Monitoring committee for attending International and national conferences, Member of the committee to design curricula of Int MTech program, Associate Dean (Faculty Affairs) IIT Patna