References

For the Uhlenbeck Lecture:

1. Serre’s chapter on modular forms in “A course in arithmetic”.
2. Fred Diamond and Jerry Shurman “A first course in modular forms”
3. The video of Frank Calegari’s plenary ICM address in 2022: https://www.youtube.com/watch?v=EDsK-8SBx-g
4. The article “Langlands reciprocity: L-functions, automorphic forms, and Diophantine equations” by Matt Emerton that was published in a collection called “The genesis of the Langlands program”. (This is more for a historical perspective and one does not need to follow everything in the article, but it can be used as a guide for how different objects are supposed to be related.)  The article is available here: https://math.uchicago.edu/~emerton/pdffiles/reciprocity.pdf
5. “Fermat’s last theorem" by Diamond, Darmon and Taylor, available here: https://www.math.mcgill.ca/darmon/pub/Articles/Expository/05.DDT/paper.pdf

For more advanced references:
1. Scholze (ICM 2018), available here: https://people.mpim-bonn.mpg.de/scholze/Rio.pdf
2. Thorne (ECM 2022), available here: https://content.ems.press/assets/public/full-texts/books/262/chapters/online-pdf/978-3-98547-551-3-chapter-5175.pdf
3. “Recent progress on Langlands reciprocity for GL_n: Shimura varieties and beyond”,  that I wrote jointly with Sug Woo Shin, available here: https://www.ma.imperial.ac.uk/~acaraian/papers/IHES-Caraiani-Shin.pdf
4. “Perfectoid spaces: lectures from the 2017 Arizona Winter School".

For the Terng Lecture:

Books:
1. Linear Representations of Finite Groups (Serre)
2. Representations of SL2(Fq) (Bonnafe)
3a. Representations of Finite Chevalley Groups (Srinivasan)
3b. Representations of Finite Groups of Lie Type (Digne, Michel)
3c. The Character Theory of Finite Groups of Lie Type (Geck, Malle)
4. Characters of Reductive Groups over a Finite Field (Lusztig)
5. The Local Langlands Conjecture for GL(2) (Bushnell, Henniart)

Papers:
1. The characters of the finite symplectic group Sp(4,q) (Srinivasan)
2. Representations of reductive groups over finite fields (Deligne, Lusztig)
3. Représentations linéaires des groupes finis "algébriques", d’après Deligne-Lusztig (Serre)
4. Character sheaves, I (Lusztig)
5. Character sheaves (Mars, Springer)
6. Reductive groups over local fields (Tits)
7a. Unrefined minimal K-types for p-adic groups (Moy, Prasad)
7b. Jacquet functors and unrefined minimal K-types (Moy, Prasad)
8. On non-abelian Lubin-Tate theory via vanishing cycles (Yoshida)

Note: Reading these sources is not a prerequisite! If it will make you happy, please use this list to contextualize the subject of the course.