Real Algebraic Geometry (in particular Positive Polynomials and Sum of Squares, Invariant Theory)
Invariant Nonnegative Forms vs Sums of Squares
Pythagorous numbers and Polynomial identities
Reviewer for Journal / Conference
C. Goel, "Cones in and around the Sums of Squares cone", to appear in Real algebraic geometry with a view toward Hyperbolic Programming and Free Probability, Mathematisches Forschungsinstitut Oberwolfach Report 2020. (DOI: 10.4171/OWR/2020/12)
C. Goel, "Invariant Nonnegative forms as Sums of Squares", Extended abstract from the workshop "Real algebraic geometry with a view toward moment problems and optimization", Mathematisches Forschungsinstitut Oberwolfach Report, Volume 14 (2017), Issue 1, 771-862.
C. Goel, S. Kuhlmann, B. Reznick, "The analogue of Hilbert's 1888 theorem for Even Symmetric Forms", Journal of Pure and Applied Algebra (2017), 221, 1438-1448.
C. Goel, S. Kuhlmann, B. Reznick, "On the Choi-Lam analogue of Hilbert's 1888 theorem for Symmetric Forms", Linear Algebra and its Applications (2016), 496, 114-120.
C. Goel, "Extension of Hilbert's 1888 Theorem to Even Symmetric Forms", Dissertation (2014), University of Konstanz, available on Konstanzer Online-Publikations-System, 1-142.
Ms. Sarah Tanja Hess - ongoing(at University of Konstanz Germany - joint with Prof. Dr. Salma Kuhlmann)
Ms. Kalyani Pendke - ongoing
Ms. Ankita Umale - ongoing
B.E. / B. Tech
Head of the Department, Basic Sciences, IIIT Nagpur
Chairperson of the Board of Studies of Basic Sciences Department at IIIT Nagpur.
Nodal Officer for implementing IRINS (Indian Research Information Network System) and the Plagiarism Development Software URKUND at IIIT Nagpur, funded by MHRD. (2019 - June 2020)
Member of Senate at IIIT Nagpur
Member of Library Management Committee at IIIT Nagpur
Member of Anti Ragging committee at IIIT Nagpur
Member of Sexual Harassment Committee at IIIT Nagpur
Admission Committee member at IIIT Nagpur
Any Other :
Organized "International Webinar - Celebrating Women in Mathematics (in honour of Maryam Mirzakhani)" on May 29, 2021, at IIIT Nagpur. More information
Recipient of "Oberwolfach Foundation Fellowship" and "Oberwolfach Leibnitz Fellowship" from Mathematisches Forschungsinstitute Oberwolfach, Germany.
Member of European Women in Mathematics (EWM)
Professional working proficiency (level C1) in German language and elementary proficiency (level A1) in the French language
Organized "International Webinar - Celebrating Women in Mathematics (in honour of Maryam Mirzakhani)" on May 29, 2020, at IIIT Nagpur. More information
Organised "Tagung: Konstanz - Women in Mathematics 2015" (together with S. Kuhlmann) on June 19, 2015, at University of Konstanz, Germany. More information