Research

Research Areas

The school covers diverse research areas, ranging from applied math closely related to advanced technologies to pure math of the most abstract form.Within our school we have 9 loosely defined research groups, with overlapping facultymembers:

ALGEBRA AND NUMBER THEORY

We have a group of young researchers active in algebraic geometry, number theory, and representation theories of associative algebras and Lie algebras.

Algebraic geometry studies the common zeroes of polynomials in several variables (algebraic varieties). It has evolved from its classical beginning to a deep subject interconnected with many different fields. Methods from topology, differential geometry and complex analysis are regularly applied in algebraic geometry. The quest for integral or rational solutions links it closely with number theory. One research topic studied in Wuhan University is abelian varieties, which are higher generalizations of elliptic curves. Other topics of interest include algebraic surfaces, fibration theory, and Poisson geometry.

Number theory is often called the queen of mathematics. In the last few decades, research in number theory has seen rapid developments and breakthroughs in multiple fronts. The nature of integral or rational solutions of polynomial equations depend on the geometry of the underlying varieties, an interplay forming the central theme of arithmetic geometry. Meanwhile, representation techniques are ubiquitous in Wiles’ proof of Fermat’s Last Theorem and the Langlands program. Analytic number theory is the study of the distribution of prime numbers，boasting profound conjectures like the Riemann Hypothesis. Researches are conducted in analytical and combinatorial number theory, such as automorphic forms, enumerative combinatorics, analytic combinatorics, the partition theory, hypergeometric series and q-series.

Representation theory studies symmetries in linear spaces. It is a beautiful mathematical subject with far reaching applications, ranging from geometry and number theory to mathematical physics. One research topic in Wuhan University is representation theory of associative algebras and triangulated categories, characterizing various (representation-finite, tame, wild) types of algebras, and classifying their indecomposable representations. Another topic is representation theory of vertex operator algebras, which arises from the study of Kac-Moody Lie algebras and the Monster group. Researches are also carried out on the representation theory of reductive groups over local fields, particularly in the algebraic aspect of Langlands program.

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