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• PhD in Mathematics from University of Konstanz, Germany (2014)
• CT3-Probability & Mathematical Statistics certificate from Institute of Actuaries of India (2009)
• M.Sc. (Honours School) Mathematics from Panjab University, Chandigarh, India (2008)
• B.Sc. (Honours School) Mathematics from Panjab University, Chandigarh, India (2006)

• 2018 to till date - Assistant Professor, IIIT Nagpur
• August 2017 - May 2018 - Adjunct Assistant Professor, VNIT Nagpur
• Since May 2017: Vrijwillig academisch medewerker (voluntary academic staff member) at the Department of Mathematics-Computer Science, University of Antwerp, Belgium more details
• May 2016 - August 2017 - Postdoctoral Research Associate, IISER Mohali
• May 2015 - April 2016 - Associated Fellow of Zukunftskolleg at University of Konstanz, Germany
• August 2014 - December 2015 - Postdoctoral Research Fellow and Academic Assistant, University of Konstanz
• August 2013 - December 2015 - Academic Assistant in the Research project: Information- und Gesprächsplattform "Frauen in der Mathematik: Wege in Studium und Beruf", University of Konstanz
• October 2012 - July 2013 - Academic Assistant at the Department of Mathematics and Statistics, University of Konstanz
• August 2011 - September 2012 - Research Assistant in the Research project "Real Algebraic Geometry and Emerging Applications", University of Konstanz
• April 2010 - July 2011 - Student Assistant at the Lehrstuhl of Prof. Dr. S. Kuhlmann, Department of Mathematics and Statistics, University of Konstanz

Link to IRINS/Vidwan Research Profile

• Area of Research

• Real Algebraic Geometry (in particular Positive Polynomials and Sum of Squares, Invariant Theory)
• Quadratic forms
• Polynomial Optimization

• Research Project

• Invariant Nonnegative Forms vs Sums of Squares
• Pythagorous numbers and Polynomial identities

• Reviewer for Journal / Conference

• Zentralblatt MATH

• 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.

• PhD.
  • Ms. Sarah Tanja Hess - ongoing (at University of Konstanz Germany - joint with Prof. Dr. Salma Kuhlmann) 
  • Ms. Kalyani Pendke  - ongoing
  • Ms. Ankita Umale - ongoing
• M. Tech.
• 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