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Generative Artificial Intelligence (GenAI) offers numerous opportunities to revolutionise teaching and learning in Computing Education (CE). However, educators have expressed concerns that students may over-rely on GenAI and use these tools to generate solutions without engaging in the learning process. While substantial research has explored GenAI use in CE, and many Computer Science (CS) educators have expressed their opinions and suggestions on the subject, there remains little consensus on implementing curricula and assessment changes. In this paper, we describe our experiences with using GenAI in CS-focused educational settings and the changes we have implemented accordingly in our teaching in recent years since the popularisation of GenAI. From our experiences, we propose two primary actions for the CE community: 1) redesign take-home assignments to incorporate GenAI use and assess students on their process of using GenAI to solve a task rather than simply on the final product; 2) redefine the role of educators to emphasise metacognitive aspects of learning, such as critical thinking and self-evaluation. This paper presents and discusses these stances and outlines several practical methods to implement these strategies in CS classrooms. Then, we advocate for more research addressing the concrete impacts of GenAI on CE, especially those evaluating the validity and effectiveness of new teaching practices., Comment: Accepted to ACE'25

CG (Computer Graphics) is a popular field of CS (Computer Science), but many students find this topic difficult due to it requiring a large number of skills, such as mathematics, programming, geometric reasoning, and creativity. Over the past few years, researchers have investigated ways to harness the power of GenAI (Generative Artificial Intelligence) to improve teaching. In CS, much of the research has focused on introductory computing. A recent study evaluating the performance of an LLM (Large Language Model), GPT-4 (text-only), on CG questions, indicated poor performance and reliance on detailed descriptions of image content, which often required considerable insight from the user to return reasonable results. So far, no studies have investigated the abilities of LMMs (Large Multimodal Models), or multimodal LLMs, to solve CG questions and how these abilities can be used to improve teaching. In this study, we construct two datasets of CG questions requiring varying degrees of visual perception skills and geometric reasoning skills, and evaluate the current state-of-the-art LMM, GPT-4o, on the two datasets. We find that although GPT-4o exhibits great potential in solving questions with visual information independently, major limitations still exist to the accuracy and quality of the generated results. We propose several novel approaches for CG educators to incorporate GenAI into CG teaching despite these limitations. We hope that our guidelines further encourage learning and engagement in CG classrooms., Comment: 8 pages, 8 figures, 1 table, to be published in SIGGRAPH Asia 2024 Educator's Forum

We survey several recent examples of derived structures emerging in connection with the Langlands correspondence. Cases studies include derived Galois deformation rings, derived Hecke algebras, derived Hitchin stacks, and derived special cycles. We also highlight some open problems that we expect to be important for future progress., Comment: Written for the proceedings of the 2022 IHES summer school. Comments and corrections appreciated!

Higher theta series on moduli spaces of Hermitian shtukas were constructed by Feng--Yun--Zhang and conjectured to be modular, parallel to classical conjectures in the Kudla program. In this paper we prove the modularity of higher theta series after restriction to the generic locus. The proof is an upgrade, using motivic homotopy theory, of earlier work of Feng--Yun--Zhang which established generic modularity of $\ell$-adic realizations. In the process, we develop some general tools of broader utility. One such is the "motivic sheaf-cycle correspondence", a categorical trace formalism for extracting computations in the Chow group from computations in Voevodsky's derived category of motives. Another new tool is the "derived homogeneous Fourier transform", which we use to implement a form of Fourier analysis for motives., Comment: Corrected some statements in section 7.5. This paper absorbs arXiv:2311.13270 as section 8

We study conjectures of Ben-Zvi--Sakellaridis--Venkatesh that categorify the relationship between automorphic periods and $L$-functions in the context of the Geometric Langlands equivalence. We provide evidence for these conjectures in some low-rank examples, by using derived Fourier analysis and the theory of chiral algebras to categorify the Rankin-Selberg unfolding method., Comment: Some corrections

We develop a theory of Smith-Treumann localization and relative parity sheaves in the context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We then apply this theory to prove some conjectures of Treumann-Venkatesh concerning mod-$\ell$ Local Langlands functoriality between a reductive group $G$ and its fixed subgroup under an order $\ell$ automorphism. As another application, we calculate the Fargues-Scholze parameters of mod-$\ell$ Howe-unramified toral representations., Comment: Substantive corrections to Section 5, plus minor revisions elsewhere

The Breuil-M\'{e}zard Conjecture predicts the existence of hypothetical "Breuil-Mezard cycles" in the moduli space of mod $p$ Galois representations of $\mathrm{Gal}(\overline{\mathbb{Q}}_q/\mathbb{Q}_q)$ that should govern congruences between mod $p$ automorphic forms. For generic parameters, we propose a construction of Breuil-M\'{e}zard cycles in arbitrary rank, and verify that they satisfy the Breuil-M\'{e}zard Conjecture for all sufficiently generic tame types and small Hodge-Tate weights. Our method is purely local and group-theoretic, and completely distinct from previous approaches to the Breuil-M\'ezard Conjecture. In particular, we leverage new connections between the Breuil-M\'ezard Conjecture and phenomena occurring in homological mirror symmetry and geometric representation theory., Comment: The earlier version contained an error in what was formerly Section 5, which has now be excised. Several corrections, clarifications, and explanations added to Appendix B. Some minor notational adjustments to Section 10. A few typos corrected throughout, especially in Section 10

In a previous paper we constructed $\textit{higher}$ theta series for unitary groups over function fields, and conjectured their modularity properties. Here we prove the generic modularity of the $\ell$-adic realization of higher theta series in cohomology. The proof debuts a new type of Fourier transform, occurring on the Borel-Moore homology of moduli spaces for shtuka-type objects, that we call the $\textit{arithmetic Fourier transform}$. Another novelty in the argument is a $\textit{sheaf-cycle correspondence}$ extending the classical sheaf-function correspondence, which facilitates the deployment of sheaf-theoretic methods to analyze algebraic cycles. Although the modularity property is a statement within classical algebraic geometry, the proof relies on derived algebraic geometry, especially a nascent theory of $\textit{derived Fourier analysis}$ on derived vector bundles, which we develop.

We sketch the construction of a derived enhancement of the reciprocity isomorphism of class field theory. Details will appear in a forthcoming joint paper of the authors with A. Raksit., Comment: In memory of John Coates

Brou\'{e}'s Abelian Defect Conjecture predicts interesting derived equivalences between derived categories of modular representations of finite groups. We investigate a generalization of Brou\'{e}'s Conjecture to ring spectrum coefficients and prove this generalization in the cyclic defect case, following an argument of Rouquier., Comment: 34 pages, comments welcome!

Let $G$ be a split semi-simple group over a global function field $K$. Given a cuspidal automorphic representation $\Pi$ of $G$ satisfying a technical hypothesis, we prove that for almost all primes $\ell$, there is a cyclic base change lifting of $\Pi$ along any $\mathbb{Z}/\ell\mathbb{Z}$-extension of $K$. Our proof does not rely on any trace formulas; instead it is based on modularity lifting theorems, together with a Smith theory argument to obtain base change for residual representations. As an application, we also prove that for any split semisimple group $G$ over a local function field $F$, and almost all primes $\ell$, any irreducible admissible representation of $G(F)$ admits a base change along any $\mathbb{Z}/\ell\mathbb{Z}$-extension of $F$. Finally, we characterize local base change more explicitly for a class of representations called toral supercuspidal representations., Comment: Minor revisions