About

I am an alumni studying the talented program in Mathematics at Vietnam National University of Science. I finished my Master 2 study in Mathematics, Algebra and Geometry parcour at Université de Rennes 1, France. Currently, I am PhD student, also at Rennes 1.

This is my blog where I write about myself and my interests. See more on my personal site.

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  1. MDNFromVNlúc 06:20 17 tháng 2, 2025

    Seeing you on Facebook, it is great to see a vietnamese guy actually passionate about mathematics

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  2. MDNFromVNlúc 21:46 17 tháng 2, 2025

    Prob yes, but the ratio between pure/applied is quite unbalance, people may like doing something like from integration to ODE,PDE, .. but I dont often meet people irl ( I havent seen anyone) doing topology or abstract algebra passionately.

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    1. Pham Khoa Banglúc 21:59 17 tháng 2, 2025

      Bạn nên học cách đặt dấu câu cho chuẩn trước khi học toán. Và chẳng có lý do gì mong có thêm người học toán chứ chưa nói tới sự mất cân bằng nhân lực giữa các ngành.

      Xóa
    2. MDNFromVNlúc 01:56 18 tháng 2, 2025

      Sorry, i don't mean to offense anyone for not doing math, just sharing my view about the world around me , which makes me a bit lonely, so that's why i commented on your blog because i just never saw anyone like you before.

      Xóa

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Affine Grassmannians of reductive groups

This serves as a starting point for my self-study of geometric Langlands. Currently, I am interested in geometric Satake equivalence, which establishes an equivalence between the category of representation of the Langland dual group (of a given reductive group) and the category of perverse sheaves on affine Grassmannians. Affine grassmannians are interesting objects, and appear naturally when studying stack of principal bundles. Let us now study them, and the story, of reductive groups, is often with $\mathrm{GL}_n$.  Affine Grassmannians of general linear groups via lattices Let $R$ be a commutative ring and denoteby $R[[t]]$ and $R((t))$ the formal power series and Laurent series, respectively.  Definition . A lattice $L \subset R((t))^n$ is a finite locally free $R[[t]]$-submodule of $R((t))^n$ such that the canonical morphism $L \otimes_{R[[t]]} R((t)) \longrightarrow R((t))^n$ is an isomorphism. Note that locally free means that a vector bundle at the level of schemes...
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Potential semi-stability of p-adic representations coming from algebraic geometry

Last week, I participated in a summer school on arithmetic geometry and Langlands program. Although this is not my field of interests, I always give some respect those who work in those fields. I also did gave a motivational TA talk about couting points on elliptic curves. To be honest, I do not expect to learn much from this school but I got enough inspiration to read arithmetic stuff, which I am going to write. Since I am an algebraic geometer, I'd like to present things in a geometric way. Let $p$ be a prime number and denote $\mathbb{Q}_p$ the $p$-adic local field. Let $K$ be a finite extension of $\mathbb{Q}_p$. Let $G_K = \mathrm{Gal}(\overline{K}/K)$ the absolute Galois group. A $\ell$- adic representation of $G_K$ is a continuous morphism (of groups) $$G_K \longrightarrow \mathrm{GL}_n(V),$$ where $V$ is a finite-dimensional $\mathbb{Q}_{\ell}$-vector space with $\ell \neq p$ a prime. We denote by $K^{unr}$ the maximal unramified extension and $I_K = \mathrm{Gal}(\overline...
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Drinfeld curves and geometric Mackey Formula

This blog serves as my preparation for my talk at Bloch's seminar workshop on Deligne-Lusztig varieties. I will present a talk about $\ell$-adic cohomology of Drinfeld curves, which are easiest examples of Degline-Lusztig varieties. To begin with, the story dates back to representation theory of finite group of Lie type (by a finite group of Lie type, I mean $G^F$ with $G$ a reductive group over a finite field and $F$ the Frobenious endomorphism). To say why these groups are important, it is the classification of finite simple groups saying that any finite simplegroup belongs to four classes: cyclic, alternating, $26$ sporadic groups, and the others are all of Lie type.  The central object of this blog is $SL_2(\mathbb{F}_q)$ with $q=p^r$ a prime power. It is a finite group of Lie type whose cardinality is $q(q-1)(q+1)$ (it's a fun exercise to show this in case you do not know). Not only $SL_2(\mathbb{F}_q)$, but the representation theory of any finite group over complex numbe...
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