In the Spring Undergraduate seminar the participants studying through recommended books. Topics: (Reference for questions)

- Algebraic Topology: A. Hatcher, Algebraic Topology, Chapter 2 and 3. (Prof. Shi Wang)
- Hodge Theory: Claire Voisin, Hodge Theory and Complex Algebraic Geometry I, Chapter 5 to 8 (Prof. Ziyuan Ding)
- Algebraic number theory and local class field theory: J. Neukirch, Algebraic number theory, Chapter 2 to 5, J.-P. Serre, Local fields, as a related reference, (Prof. Daniel Skodlerack)
- Smooth representation theory and local Langlands: Bushnell-Henniart, Local Langlands for GL(2) (Prof. Daniel Skodlerack)
- Non-linear dispersive equations: J. Duoandikoetxea, Fourier Analysis, Chapter 1 to 5, Chapter 8; and T. Tao,, Nonlinear dispersive equations, Chapter 1 to 3 (Prof. Haitian Yue)

The students give a regular report on their reading.

Tuesdays 6pm-7:40pm, IMS S506 **Starting at March the 5th. **

**Talks: **

- March 5th: Report on reading on p-adic numbers, Topic 3. "Non-Archimedian valuations and completions" (Yulun Wu)
- March 12th on Topic 1: Section 3.1.1 "Cohomology groups and the Universal Coeffiecient Theorem" (Yiyang Gong)
- March 19th on Topic 2: Chapter 5 "Harmonic forms and Cohomology" (Yutong Li)
- March 26th on Topic 3 (related): "Mordell's Theorem" (Jiande Zhang)
- April 2nd on Topic 5: "Fourier transform and Sobolev spaces" (Liang Shang)
- April 9th on Topic 3: "Extending p-adic absolute value on finite extensions of Q_p and normed vector spaces". (Yulun Wu)
- April 16th on Topic 1: Section 3.1.2: "Cohomology of spaces" (Yiyang Gong)
- April 23rd on Topic 2: Chapter 6 "Hodge theory in Case of Kähler manifolds" (Yutong Li)
- April 30th on Topic 3: "Conics and p-adic numbers" (Jiande Zhang)
- May 7th on Topic 5: "Hardy-Littlewood maximal operator and singular integrals" (Liang Shang)
- May 14th on Topic 3 (Yulun Wu)
- May 21st on Topic 1 "The cup product" (Yiyang Gong)
- May 28th on Topic 2 "Singular integrals" (Liang Shang)
- June 4th on Topic 3 (Jiande Zhang)
- June 11th on Topic 5 (Yutong Li)