In my research, I study interactions between number theory, algebra and geometry of orders in algebras
over global fields, in particular, in quaternion algebras. Studies of these interactions involve number theory (in particular of lattices in quadratic spaces), arithmetic algebraic geometry and purely algebraic properties of orders in algebras. I also like to work with number theoretical problems in which numerical, computer related, experiments give new insights into interesting mathematical results through new examples or new mathematical evidence, which sometimes can be theoretically verified.
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