Eslam Badr earned his PhD from Universitat Autonoma de Barcelona (UAB) in Spain before joining the AUC. His area of expertise is within algebraic geometry and arithmetic. More specifically, his research mainly deals with explicit geometric and arithmetic properties of smooth plane curves/hypersurfaces and their moduli spaces. Topics including but not limited to: automorphism groups, twisting theory, fields of definition versus the field of moduli, quadratic points and geometric progression sequences.
Badr is interested in teaching several mathematics courses including, Algebra and Mathematical Logic, Differential and Integral Calculus, Linear and Abstract Algebra, Ordinary Differential Equations, Galois Theory, Number Theory and, Arithmetic geometry.
- PhD in Mathematics, Universitat Autonoma de Barcelona, Spain (2017)
- MSc in Mathematics, Faculty of Science, Cairo University (2013)
- BSc in Mathematics, Faculty of Science, Cairo University (2010)
- “On the locus of smooth plane curves with a fixed automorphism group”. Mediterr. J. Math. 13, No. 5 (2016), 3605-3627.
- “Automorphism groups of non-singular plane curves of degree 5”. Commun. Algebra 44 (10), 2016, 4327-4340.
- "Plane non-singular curves with an element of “large” order in its automorphism group”. Int. J. Algebra Comput. 26 (2), 2016, 399-434.
- “Riemann surfaces defined over the reals”. Arch. Math. 110 (2018), 351-362.
- “The Picard Group of Brauer-Severi Varieties”. Open Math. (formerly Central European Journal of Mathematics) 16 (2018), 1196-1203.
- “On twists of smooth plane curves”. Math. Comput. 88 (2019), 421-438.
- “Plane model-fields of definition, fields of definition, the field of moduli of smooth plane curves”. J. Number Theory 194 (2019), 278-282.
- “A note on the stratification of smooth plane curves of genus 6”. Colloq. Math. 192, (2020), 207-222.
- “Hypersurface model-fields of definition for smooth hypersurfaces and their twists”. Acta Arith. 194, (2020), 267-280.
- “A class of pseudoreal Riemann surfaces with diagonal automorphism group”. Algebra Colloq. 27, (2020), 247-262.
- “On quadratic progression sequences on smooth plane curves”. J. Number Theory 213, (2020), 445-452.
- “Bielliptic smooth plane curves and quadratic points”. Int. J. Number Theory 17, (2021), 1047-1066.
- Automorphism groups
- Twisting theory
- Fields of definition versus the field of moduli
- Quadratic points and geometric progression sequences
- Weierstrass points