黄炳荣山东大学主页平台管理系统--中文主页

L-functions

Spring 2024, Jinan

Time and Place:

Tuesday 14:00-16:00, 逸夫信息楼 A403.

Instructors:

Bingrong Huang and Yongxiao Lin

Prerequisites:

Basic Analytic Number Theory and Automorphic Forms.

Syllabus:

This is a reading course. We plan to read the following chapters and papers in this semester.

[BFKMMS] Blomer, Valentin; Fouvry, Étienne; Kowalski, Emmanuel; Michel, Philippe; Milićević, Djordje; Sawin, Will. The second moment theory of families of L-functions—the case of twisted Hecke L-functions. Mem. Amer. Math. Soc. 282 (2023), no. 1394, v+148 pp. MR4539366

[FKMS] Fouvry, Étienne; Kowalski, Emmanuel; Michel, Philippe; Sawin, Will. Lectures on applied ℓ-adic cohomology. Analytic methods in arithmetic geometry, 113–195, Contemp. Math., 740, Centre Rech. Math. Proc., Amer. Math. Soc., [Providence], RI, [2019], ©2019. MR4033731

Schedule:

Date	Speaker	Title	References
February 27	Yongxiao Lin	Momemts of L-functions	[BFKMMS] Chap. 1
March 05	Yongxiao Lin	Momemts of L-functions, II	[BFKMMS] Chap. 1
March 12	Chenyang Lu	L-functions	[BFKMMS] Chap. 2
March 19	Chenyang Lu	L-functions, II	[BFKMMS] Chap. 2
March 26	Bin Guan	Local Langlands conjecture
April 02	Liangxun Li	The twisted moments	[BFKMMS] Chap. 4
April 09	Liangxun Li	The twisted moments, II	[BFKMMS] Chap. 5
April 16	Liangxun Li	The +ab shift	[FKMS] Sec. 16
April 23	Zhehao He	Non-vanishing	[BFKMMS] Chap. 6
April 30	Zhehao He	Non-vanishing, II	[BFKMMS] Chap. 6
May 07	Jiangpeng Li	Extreme values	[BFKMMS] Chap. 7
May 14	Jinghai Liu	The analytic rank	[BFKMMS] Chap. 8
May 21	Zhenyu Zhang	Modular symbols	[BFKMMS] Chap. 9
May 28	Haozhe Gou	Algebraic exponential sums	[BFKMMS] Chap. 3
June 04
June 11
June 18

Contact:

Bingrong Huang (Email: brhuang (AT) sdu.edu.cn; Office: Mingde Building C701)

Yongxiao Lin (Email: yongxiao.lin (AT) sdu.edu.cn; Office: Mingde Building C705)

模形式讨论班

2023年秋季学期

教材：

[Bump]. Bump, Daniel. Automorphic forms and representations. Cambridge Studies in Advanced Mathematics, 55. Cambridge University Press, Cambridge, 1997. xiv+574 pp. 第一章

[Sarnak]. Sarnak, Peter. Some applications of modular forms. Cambridge Tracts in Mathematics, 99. Cambridge University Press, Cambridge, 1990. x+111 pp.

参考书：

[Iwaniec]. Iwaniec, Henryk. Topics in classical automorphic forms. Graduate Studies in Mathematics, 17. American Mathematical Society, Providence, RI, 1997. xii+259 pp.

时间地点：

中心校区知新楼B座119，每周五晚上 19:00-21:50

讲课安排：

时间	讲课人	讲课内容	参考
2023-09-08	黄炳荣	模形式简介
2023-09-15	王可	Dirichlet L-functions	[Bump, Sect. 1.1]
2023-09-22	李良汛	The modular group	[Bump, Sect. 1.2]
2023-09-29	中秋节放假
2023-10-06	国庆节放假
2023-10-13	刘子铭	Modular forms for SL(2,Z)	[Bump, Sect. 1.3]
2023-10-20	王海旭	Hecke operators	[Bump, Sect. 1.4]
2023-10-27	吕章印	Twisting	[Bump, Sect. 1.5]
2023-11-03	卢浩阳	The Rankin-Selberg method	[Bump, Sect. 1.6]
2023-11-10	张璕	Hecke characters and Hilbert modular forms	[Bump, Sect. 1.7]
2023-11-17	刘天	Artin L-functions and Langlands functoriality	[Bump, Sect. 1.8]
2023-11-24	宋卓奇	Maass forms	[Bump, Sect. 1.9]
2023-12-01	孙伟涛	Base change	[Bump, Sect. 1.10]
2023-12-08	李晓承	Poincare series	[Sarnak, Sect. 1.3 & 1.5]
2023-12-15	郭诚亮	Kloosterman sums	[Sarnak, App. 1.1-1.2]
2023-12-22	张振宇	Ramanujan bounds	[Sarnak, Chap. 4]

Contact: Bingrong Huang (Email: brhuang@sdu.edu.cn, Office : Mingde Building C701).

Course homepage: https://faculty.sdu.edu.cn/brhuang/zh_CN/zdylm/1626738/list/index.htm

L-functions

Spring 2023, Jinan

Time and Place:

Wednesday 10:10-12:00, Math Building 204.

Prerequisites:

Basic Analytic Number Theory and Automorphic Forms.

Syllabus:

This is a reading course. We plan to read the following chapters and papers in this semester.

[Iw02] Iwaniec, H. Spectral methods of automorphic forms. Second edition. Graduate Studies in Mathematics, 53. American Mathematical Society, Providence, RI; Revista Matemática Iberoamericana, Madrid, 2002. xii+220 pp. Chapters 11-13.

[CI00] Conrey, J. B.; Iwaniec, H. The cubic moment of central values of automorphic L-functions. Ann. of Math. (2) 151 (2000), no. 3, 1175–1216.

[PY20] Petrow, I.; Young, Matthew P. The Weyl bound for Dirichlet L-functions of cube-free conductor. Ann. of Math. (2) 192 (2020), no. 2, 437–486.

Schedule:

Date	Speaker	Title	References
February 15	Liangxun Li	The distribution of eigenvalues, I	[Iw02, Chap. 11]
February 22	Jinzhi Feng	The distribution of eigenvalues, II	[Iw02, Chap. 11]
March 1	Meijie Lu	Hyperbolic lattice point problems	[Iw02, Chap. 12]
March 8	Shu Luo	Spectral bounds for cusp forms	[Iw02, Chap. 13]
March 15	Bingrong Huang	Introduction	[CI00]
March 22	Liangxun Li	Automorphic forms and L-functions	[CI00] §2-7
March 29	Liangxun Li	Estimation of the c ubic moments	[CI00] §9-10
April 5	Qingming Festival
April 12	Liangxun Li	Separation of variables	[CI00] §8
April 19	Liangxun Li	Bilinear forms	[CI00] §11-12
April 26	Liangxun Li	Estimation of the character sums	[CI00] §13-14
May 03	Labor Day
May 10	Shu Luo	Sect. 1	[PY20]
May 17	Jinzhi Feng	Sect. 2-4	[PY20]
May 24	Zhenyu Zhang	Sect. 5-8	[PY20]
May 31	Shenghao Hua	Sect. 9	[PY20]
June 07	Shenghao Hua		[PY20]
June 14	Meijie Lu

Contact: Bingrong Huang (Email: brhuang@sdu.edu.cn; Office: Mingde Building C701)

Course homepage: https://faculty.sdu.edu.cn/brhuang/zh_CN/zdylm/1592228/list/index.htm

A first course in sieve methods

Fall 2022 ＆ Spring 2023, Jinan

Organizers:

Shenghao Hua, Bingrong Huang, Zhiwei Wang.

Time and Place:

Fall 2022: Thursday 14:00-16:00, Zhixin Building B1044.

Spring 2023: TBA

Prerequisites:

Elementary Number Theory.

Synopsis:

This is a reading seminar. We plan to read Friedlander and Iwaniec’s sieve method book Opera de cribro, and some applications of sieve methods and large sieve methods, such as Goldbach’s Conjecture, Twin Prime Conjecture, and so on. This is also a joint course with Professor Zhiwei Wang’s Advanced Analytic Number Theory course in Fall 2022.

Reference:

[Chen66]. Chen Jing-run. On the representation of a large even integer as the sum of a prime and the product of at most two primes. Kexue Tongbao 17 (1966), 385–386.

[FI10]. Friedlander, John; Iwaniec, Henryk. Opera de cribro. American Mathematical Society Colloquium Publications, 57. American Mathematical Society, Providence, RI, 2010.

[FI09]. Friedlander, John; Iwaniec, Henryk. What is … the parity phenomenon? Notices Amer. Math. Soc. 56 (2009), no. 7, 817–818.

[HR74].Halberstam, H.; Richert, H.-E. Sieve methods. London Mathematical Society Monographs, No. 4. Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1974.

[Maynard15]. Maynard, James. Small gaps between primes. Ann. of Math. (2) 181 (2015), no. 1, 383–413.

[Zhang14]. Zhang, Yitang. Bounded gaps between primes. Ann. of Math. (2) 179 (2014), no. 3, 1121–1174.

Automorphic forms

Fall 2022, Jinan

Time and Place:

Thursday 09:00-12:00, Zhixin Building B1044.

Prerequisites:

Basic Analytic Number Theory and Modular Forms.

Syllabus:

We plan to give lectures on automorphic forms in this semester. We will use the following book:

Iwaniec, Henryk. Spectral methods of automorphic forms. Second edition. Graduate Studies in Mathematics, 53. American Mathematical Society, Providence, RI; Revista Matemática Iberoamericana, Madrid, 2002. xii+220 pp.

Schedule:

Week	Date	Contents
1	Sep. 08	No class
2	Sep. 15	Introduction; The upper half plane and Group decompositions
3	Sep. 22	The Laplace operator and eigenfunctions
4	Sep. 29	The invariant integral operators and Green functions
5	Oct. 06	Fuchsian groups
6	Oct. 13	Kloosterman sums
7	Oct. 20	Automorphic forms
8	Oct. 27	The spectral theorem of discrete part
9	Nov. 03	The automorphic Green function
10	Nov. 10	Analytic continuation of the Eisenstein series
11	Nov. 17	The spectral theorem of continuous part
12	Nov. 24	Averages of Fourier coefficients
13	Dec. 01	Kuznetsov trace formula
14	Dec. 08	Selberg trace formula
15	Dec. 15	Selberg trace formula, II
16	Dec. 22	Weyl's law

Contact: Bingrong Huang (Email: brhuang@sdu.edu.cn; Office: Mingde Building C701)

Course homepage: https://faculty.sdu.edu.cn/brhuang/zh_CN/zdylm/1477561/list/index.htm

模形式讨论班

教材：

[Serre]. Serre, J.-P. A course in arithmetic. Translated from the French. Graduate Texts in Mathematics, No. 7. Springer-Verlag, New York-Heidelberg, 1973. viii+115 pp.

[Bump]. Bump, Daniel. Automorphic forms and representations. Cambridge Studies in Advanced Mathematics, 55. Cambridge University Press, Cambridge, 1997. xiv+574 pp. 第一章

参考书：

[1]. Iwaniec, Henryk. Topics in classical automorphic forms. Graduate Studies in Mathematics, 17. American Mathematical Society, Providence, RI, 1997. xii+259 pp.

[2]. Diamond, Fred; Shurman, Jerry. A first course in modular forms. Graduate Texts in Mathematics, 228. Springer-Verlag, New York, 2005. xvi+436 pp.

[3]. Koblitz, Neal. Introduction to elliptic curves and modular forms. Second edition. Graduate Texts in Mathematics, 97. Springer-Verlag, New York, 1993. x+248 pp.

讲课安排：

时间	讲课人	讲课内容	参考
2022-09-09	黄炳荣	模形式简介
2022-09-16	朱俊辉	Finite Fields	[Serre, Chap. I]
2022-09-23	徐国瑞	p-adic Fields	[Serre, Chap. II]
2022-09-30	曹峻清	Hilbert Symbol	[Serre, Chap. III]
2022-10-07	陈沛吾	Quadratic Forms over Q_p	[Serre, Chap. IV] part 1
2022-10-14	陈沛吾	Quadratic Forms over Q	[Serre, Chap. IV] part 2
2022-10-21	李良汛	Integral Quadratic Forms	[Serre, Chap. V]
2022-10-28	郭诚亮 / 汤琰煜	PNT on APs	[Serre, Chap. VI]
2022-11-04	汤琰煜 / 吕祚政	PNT on APs, cont. / Modular Forms I	[Serre, Chap. VI] / [Serre, Chap. VII]
2022-11-11	魏子惟	Modular Forms II	[Serre, Chap. VII]
2022-11-18	宋翔宇	Modular Forms III	[Serre, Chap. VII]
2022-11-25	张振宇	Twisting	[Bump, Sect. 1.5]
2022-12-02	李响	Rankin-Selberg	[Bump, Sect. 1.6]
2022-12-09	徐国瑞	Artin and Langlands	[Bump, Sect. 1.8]
2022-12-16	黄炳荣	Maass Forms	[Bump, Sect. 1.9]

Contact: Bingrong Huang (Email: brhuang@sdu.edu.cn, Office : Mingde Building C701).

Course homepage: https://faculty.sdu.edu.cn/brhuang/zh_CN/zdylm/1477560/list/index.htm

Fundamentals in Number Theory

Spring 2022, Jinan

Schedule:

Tuesday 08:00-09:50 & Thursday 08:00-09:50.

Classroom:

Zhixin Building B124.

Prerequisites:

The first semester courses in real and complex variables, and the basic course in number theory (i.e. the first year course Basic Algebra and Geometry, see Part I of [FY]).

Syllabus:

The course is an introductory course in number theory. The topics include

1. The Euclidean algorithm, unique factorization, greatest common divisor, linear Diophantine equations, congruences, Chinese Remainder Theorem, Legendre symbol, quadratic reciprocity law, primitive roots and indices,

2. Arithmetic functions,

3. The order and average order of magnitude of arithmetic functions,

4. The distribution of primes and applications,

5. Dirichlet characters, Dirichlet's theorem on primes in arithmetic progressions,

6. Primitive characters, character sums, Polya–Vinogradov inequality,

7. Sums of squares,

8. Basic Algebraic Number Theory,

9. Diophantine approximation, continued fractions, and the transcendence of e.

If we still have time, then we may include

10. Modular forms and theta series

11. Equidistribution modulo one

Bibliography

Any introductory book on number theory will be useful. For example, see:

[L]. W.J. LeVeque, Fundamentals of Number Theory.

[P]. 潘承洞，《数论基础》.

[FY]. 冯克勤、余红兵，《整数与多项式》第一部分.

Attendance of lectures is mandatory!

Homeworks:

This will be an important part of the course. 10% of the final grade will be determined from the homework scores, which will be obtained as the average grade of a certain number of assignments.

Homework 1 (due Thursday March 3): [L] §1.1 Problems 2 & 4; §6.3 Problems 2, 3 & 6; §6.2 Problems 4; §6.1 Problems 2 & 6.

Homework 2 (due Thursday March 10): [P] 第二章习题 4, 5, 6, 7, 11, 12

Homework 3 (due Thursday March 17): [L] §6.4 Problems 3(b) & 6; §6.10 Problem 5; §6.11 Problems 2, 3, 4, 5

Homework 4 (due Thursday March 24): [L] §6.6 Problems 4, 5, & 7; §6.7 Problems 1 & 5

Homework 5 (due Thursday April 7): [L] §6.9 Problems 4, 6, & 7; §6.11 Problem 13; [P] 第三章习题 13, 14, 19

Homework 6 (due Thursday April 21): [L] §3.4 Problems 2, 6, 7, 8, & 14; §4.3 Problems 7 & 8; §5.4 Problems 2 & 3

Homework 7 (due Thursday May 5): Homework_7.pdf

Homework 8 (due Thursday May 19): Homework_8.pdf

Homework 9 (due Thursday May 26): [L] §7.3 Problems 4 & 6; §7.5 Problems 1 & 3; §8.2 Problems 3, 6, 11 & 14. (Choose 4 of them.)

Homework 10 (due Thursday June 26): [L] §8.3 Problem 4; §8.4 Problem 4; §9.1 Problem 3; §9.2 Problem 3.

Lecture notes:

Lecture note 1.pdf	Introduction	02.22
Lecture note 2.pdf	arithmetic functions	02.24, 03.01, 03.03
Lecture note 3.pdf	order of magnitude of AFs	03.08, 03.10, 03.15
Lecture note 4.pdf	the distribution of primes	03.17, 03.22, 03.29, 03.31, 04.07
[Apostol, Sections 3.8 & 5.7-5.9]	congruences and primitive roots	04.12
[LeVeque, Chapter 4]	primitive roots and indices	04,14
[Montgomery--Vaughan, Chapter 4]	Dirichlet characters	04.19, 04.21
[Iwaniec--Kowalski, Section 2.3]	Dirichlet's theorem on primes in APs	04.26, 05.03
[Montgomery--Vaughan, Chapter 9]	character sums	05.03, 05.05, 05.08
[LeVeque, Chapters 7-9]		05.12, ..., 06.09

Exercise classes: 03.24, 04.26, 05.26

Midterm exam: 04.19 or 04.21 ?? (Canceled, because of the outbreak)

Final exam: 06.20 -- 07.01

Contact: Bingrong Huang, brhuang@sdu.edu.cn, Office : Mingde Building C701

Teaching assistant: Liangxun Li, email: lxli@mail.sdu.edu.cn

Course homepage: https://faculty.sdu.edu.cn/brhuang/zh_CN/zdylm/1454369/list/index.htm

L-functions

Spring 2022, Jinan

Time and Place:

Tuesday 14:00-15:50, Mingde Building C704.

Prerequisites:

Basic Analytic Number Theory and Modular Forms.

Syllabus:

This is a reading course. We plan to read the following papers in this semester.

[S21]. Soundararajan, K. The distribution of values of zeta and L-functions. ArXiv preprint, arXiv:2112.03389, 2021.

[RS05]. Rudnick, Z.; Soundararajan, K. Lower bounds for moments of L-functions. Proc. Natl. Acad. Sci. USA 102 (2005), no. 19, 6837–6838.

[S09]. Soundararajan, K. Moments of the Riemann zeta function. Ann. of Math. (2) 170 (2009), no. 2, 981–993.

[S08]. Soundararajan, K. Extreme values of zeta and L-functions. Math. Ann. 342 (2008), no. 2, 467–486.

[RS15]. Radziwiłł, M.; Soundararajan, K. Moments and distribution of central L-values of quadratic twists of elliptic curves. Invent. Math. 202 (2015), no. 3, 1029–1068.

Schedule:

Date	Speaker	Title	References
February 22	Bingrong Huang	Moments of L-functions (Lower bounds)	[RS05]
March 1	Shenghao Hua	Values at the edge of the critical strip	[S21] §1
March 8	Shenghao Hua	Selberg's central limit theorem	[S21] §2
March 15	Yuxuan Zhou	Selberg's theorem in families of L-functions	[S21] §3
March 22	Hui Wang	Moments of L-functions	[S21] §4 & [S09]
March 29	Mingyue Fan	Conjectures of moments	[S21] §5
April 5	no talk (Qing Ming)
April 12	Mingyue Fan	Conjectures of moments	[S21] §5
April 19	Tengyou Zhu	Results on moments and FHK conjecture	[S21] §6
April 26	Tengyou Zhu	Results on moments and FHK conjecture	[S21] §8
May 03	Enxun Huang	Extreme values	[S21] §7
May 10	Enxun Huang	Extreme values	[S08]
May 17	Sizhe Xie		[RS15]
May 24	Sizhe Xie		[RS15]
May 31	Liangxun Li		[RS15]
June 07	Liangxun Li		[RS15]
June 14	Mingyue Fan		[RS15]

Contact: Bingrong Huang (Email: brhuang@sdu.edu.cn; Office: Mingde Building C701)

Course homepage: https://faculty.sdu.edu.cn/brhuang/zh_CN/zdylm/1454369/list/index.htm

Fundamentals in Number Theory

Spring 2020/21, Jinan

Schedule: Monday 10:10-12:00, Wednesday 10:10-12:00.

Classroom: Zhixin Building B119.

Prerequisites:

I will assume knowledge of the first semester courses in real and complex variables, and the basic course in number theory.

Syllabus:

The course is an introductory course in (analytic) number theory. The topics include

1. The Euclidean algorithm, unique factorization, greatest common divisor, linear Diophantine equations, congruences, Chinese Remainder Theorem, Legendre symbol, quadratic reciprocity law, primitive roots and indices

2. Arithmetic functions

3. The order and average order of magnitude of arithmetic functions

4. The Prime Number Theorem and its applications

5. Dirichlet characters, Dirichlet's theorem on primes in arithmetic progressions

6. Primitive characters, character sums, Polya–Vinogradov inequality, and Burgess' bounds

7. Sums of squares

If we still have time, then we may include (In fact, we won't have time. 06.07)

8. Modular forms and theta series

9. Equidistribution modulo one

10. Diophantine approximation, Liouville's theorem on rational approximations to algebraic numbers, Thue's equation

Bibliography

Any introductory book on number theory will be useful. For example, see:

1. W.J. LeVeque, Fundamentals of Number Theory.

2. 潘承洞，《数论基础》.

Suggested reading:

3. T. Apostol, Introduction to Analytic Number Theory.

4. H. Montgomery and R. Vaughan, Multiplicative Number Theory I. Classical Theory.

5. H. Iwaniec and E. Kowalski, Analytic Number Theory.

Attendance of lectures is mandatory!

Homeworks:

This will be an important part of the course. In order to be eligible to take the final exam, at least 50% of the assignments have to be turned in on the week of their due date. 10% of the final grade will be determined from the homework scores, which will be obtained as the average grade of a certain number of assignments.

Homework_1.pdf due Wednesday, March 17, 2021

Homework_2.pdf due Monday, March 29, 2021

Homework_3.pdf due Wednesday, April 14, 2021

Homework_4.pdf due Wednesday, April 28, 2021

Homework_5.pdf due Monday, May 17, 2021

Homework_6.pdf due Monday, May 31, 2021

Lecture notes:

Lecture note 1.pdf 03.01

Lecture note 2.pdf 03.03, 03.08, 03.10

Lecture note 3.pdf 03.10, 03.15, 03.17, 03.22

Lecture note 4.pdf 03.24, 03.29, 03.31, 04.12, 04.14

[Apostol, Sections 3.8 & 5.7-5.9] 04.19

[LeVeque, Chapter 4] 04.21

[Montgomery and Vaughan, Chapter 4] & [Iwaniec and Kowalski, Section 2.3] 04.26, 04.28, 05.08

[Montgomery and Vaughan, Chapter 9] 05.10, 05.12, 05.19, 05.24, 05.26, 05.31, 06.02, 06.07

[LeVeque, Chapter 7] 06.09

Exercise classes: 04.07, 05.17, 06.16

Contact: Bingrong Huang, brhuang@sdu.edu.cn, Office : Mingde Building C701

Teaching assistant: Shenghao Hua, huashenghao@vip.qq.com

Course homepage: https://faculty.sdu.edu.cn/brhuang/zh_CN/zdylm/1322195/list/index.htm

代数和几何基础

教材：

[1]. 冯克勤，余红兵，《整数与多项式》，高等教育出版社，施普林格出版社,1999.

[2]. 吴光磊，田畴，《解析几何简明教程 (第2版)》，高等教育出版社，2008，普通高等教育“十一五”国家级规划教材.

参考书：

[1] 潘承洞，《数论基础》，高等教育出版社，2012.

[2] 吕林根，许子道，《解析几何》第五版，高等教育出版社，2019.

Contact: Bingrong Huang, brhuang@sdu.edu.cn, Office : Mingde Building C701

Teaching assistants: Huimin Zhang and Yi Huang

Course homepage: https://faculty.sdu.edu.cn/brhuang/zh_CN/zdylm/1322196/list/index.htm

个人信息Personal Information

L-functions

Spring 2024, Jinan

Time and Place:

Instructors:

Prerequisites:

Syllabus:

Schedule:

模形式讨论班

教材：

参考书：

时间地点：

L-functions

Spring 2023, Jinan

Time and Place:

Prerequisites:

Syllabus:

Schedule:

Fall 2022 ＆ Spring 2023, Jinan

Automorphic forms

Fall 2022, Jinan

Time and Place:

Prerequisites:

Syllabus:

Schedule:

模形式讨论班

教材：

参考书：

Fundamentals in Number Theory

Spring 2022, Jinan

Schedule:

Classroom:

Prerequisites:

Syllabus:

Bibliography

Attendance of lectures is mandatory!

Homeworks:

Lecture notes:

L-functions

Spring 2022, Jinan

Time and Place:

Prerequisites:

Syllabus:

Schedule:

Fundamentals in Number Theory

Spring 2020/21, Jinan

Schedule: Monday 10:10-12:00, Wednesday 10:10-12:00.

Classroom: Zhixin Building B119.

Prerequisites:

Syllabus:

Bibliography

Attendance of lectures is mandatory!

Homeworks:

Lecture notes:

代数和几何基础

教材：

参考书：