Yunting Gao

My research interests lie in the intersection between algebra, analysis and geometry with motivation originally from mathematical physics such as calabi problem. Recently I am trying to develop the functional degree for non-commutative rings which says I am kindly switch the highlight of my research interest from global differential geometry to algebraic number theory or commutaitve algebra and use it to study the donaldson polynomials and compute the degree of those polynomials for helping us understand those algebraical structure. Also I am trying to apply technical skills from olympia math games to Discrete math problems for understanding. I am also interested in writing an introduction textbook on convex optimization. Comparing with algebra tools, I am much better at using those traditional analysis tools. I am now trying to read algebraic number

Theorist's papers such as Bhargava to diminish my horro for those very once-used technical details but creative tricks.

for getting some really original ideas. I am studying how to write a paper rather a textbook.  Now I am learning how to take a note when reading a book or a paper. I study math as a liberal art student.

String theory, algebraic geometry, non-commutative algebra, homological algebra, functional degree

Motto: Aha moment flashes up the latex screen. But I am trying to expand/improve my proof skills by using specifical examples expecially for those classical questions with my dirty hands although things which happen in the brain should be essentially the same.

Introduce or define or makes sense of  the differential forms for $\mathbb{Z}\rightarrow \mathbb{Z}$

Functional degree and its application to the classification of integer-valued functions on integers.

Research Interest: Algebraic number theory

Tutors:

1. mathematics for engineering students 2021-2022
2. first-year abstract algebra 2023-
3. Introduction to financial modelling 2023-

Past:
Non-reductive geometric invariant theory is an important topic in algebraic geometry and representation theory. Understanding geometric quotients: GIT provides a framework for constructing geometric quotients of algebraic varieties by group actions. In particular, it provides a way to construct moduli spaces of algebraic objects by taking a quotient of a space polynomial by a group action. The study of non-reductive GIT allows us to understand the strucutre of these geometric quotients in greater generality. GIT has many applications to the representation theory of algebraic groups. In particular, it is used to study the geometric of orbits and their closure in the flag varieties of semisimple algebraic groups. This leads to the study of Schubert varieties and their cohomology, which have applications to many areas of mathematics, including combinatorics and algebraic topology. Non-reductive GIT is also important in the study of algebraic geometry and algebraic topology. In particular, it provides a framework for studying equivariant cohomology, which is the cohomology of spaces with a group action. This leads to the study of equivariant Chow groups and motivic integration, which have applications to many areas of mathematics, including the study of singularities and the topology of algebraic varieties. It also has many applications to physics, especially in the study of gauge theories and string theory. In particular, it is used to study the moduli space of instantons in Yang-Mills theory and the moduli space of Higgs bundles in string theory. These moduli spaces play an important role in the study of quantum field theory and the geometric Langlands program. The study of non-reductive GIT is important because it provides a framework for understanding the geometry of group actions in algebraic varieties, and has applications to many areas of mathematics and physics. The important references in this topic are [8],[9], [10], [11], [12] and [13].
Present:
Recently I studied the Lindel ̈of principle, which is the topic in the classical complex analysis. It is found that this old topic has many applications in the potential theory. Interested readers can refer to [14],[15],[16],[17] and [18].
Plan:
My immediate plan for the future is to continue my research in the complex manifold but extend it to studying compact Kahler manifold and its relation with the stability in algebraic geometry and geometric invariant theory. More specifically, we are interested in proving the following the conjecture in with the help of the intuition idea explanation in [19]
Conjecture: A smooth polarised projective variety (V, L) admits a Kahler metric of constant scalar curvature in the class c1(L) if and only if it is K−stable.

The British Festival 2008

The Dean's List 2022

French: Beginner

German: Beginner