A Storm in a "T" Cup

We revisit the process of transversification and agglomeration of particle momenta that are often performed in analyses at hadron colliders, and show that many of the existing mass-measurement variables proposed for hadron colliders are far more closely related to each other than is widely appreciated, and indeed can all be viewed as a common mass bound specialized for a variety of purposes.Comment: 3 pages, 2 figures, presented by K.C. Kong at the 19th Particles and Nuclei International Conference, PANIC 2011, MIT, Cambridge, MA (July 24-29, 2011

Using Flow Specifications of Parameterized Cache Coherence Protocols for Verifying Deadlock Freedom

We consider the problem of verifying deadlock freedom for symmetric cache coherence protocols. In particular, we focus on a specific form of deadlock which is useful for the cache coherence protocol domain and consistent with the internal definition of deadlock in the Murphi model checker: we refer to this deadlock as a system- wide deadlock (s-deadlock). In s-deadlock, the entire system gets blocked and is unable to make any transition. Cache coherence protocols consist of N symmetric cache agents, where N is an unbounded parameter; thus the verification of s-deadlock freedom is naturally a parameterized verification problem. Parametrized verification techniques work by using sound abstractions to reduce the unbounded model to a bounded model. Efficient abstractions which work well for industrial scale protocols typically bound the model by replacing the state of most of the agents by an abstract environment, while keeping just one or two agents as is. However, leveraging such efficient abstractions becomes a challenge for s-deadlock: a violation of s-deadlock is a state in which the transitions of all of the unbounded number of agents cannot occur and so a simple abstraction like the one above will not preserve this violation. In this work we address this challenge by presenting a technique which leverages high-level information about the protocols, in the form of message sequence dia- grams referred to as flows, for constructing invariants that are collectively stronger than s-deadlock. Efficient abstractions can be constructed to verify these invariants. We successfully verify the German and Flash protocols using our technique

Noncommutative Geometry and Arithmetic

This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with complex multiplication for imaginary quadratic fields. This talk concentrates on two main aspects: the relation of Stark numbers to the geometry of noncommutative tori with real multiplication, and the shadows of modular forms on the noncommutative boundary of modular curves, that is, the moduli space of noncommutative tori. To appear in Proc. ICM 2010.Comment: 16 pages, LaTe

Predicate Abstraction with Indexed Predicates

Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model checking. We consider models containing first-order state variables, where the system state includes mutable functions and predicates. Such a model can describe systems containing arbitrarily large memories, buffers, and arrays of identical processes. We describe a form of predicate abstraction that constructs a formula over a set of universally quantified variables to describe invariant properties of the first-order state variables. We provide a formal justification of the soundness of our approach and describe how it has been used to verify several hardware and software designs, including a directory-based cache coherence protocol.Comment: 27 pages, 4 figures, 1 table, short version appeared in International Conference on Verification, Model Checking and Abstract Interpretation (VMCAI'04), LNCS 2937, pages = 267--28

Invariance: A Tale of Intellectual Migration

The plotline of the standard story told about the development of intellectual history at the end of the 19th/turn of the 20th century follows the move from absolutism to perspectivalism. The narrative takes us, on the one hand, from the scientism of late Enlightenment writers like Voltaire, Mill, D’Alebert, and Comte and the historical determinism of Hegel, all of which were based upon a universal picture of rationality, to, on the other hand, the relativistic physics of Einstein, the perspectival art of Picasso, and the individualism of Nietzsche and Kierkegaard leading to the phenomenology of Husserl and Heidegger to and on through the deconstructivist work of Derrida in which universal proclamations were deemed meaningless. In their place, was relative dependent upon subjective, political, and social factors, influences, and interpretations. Like all sketches, of course, the story is more complicated than that. There is another trend in the intellectual air of the early 20th century that gets left out of this oversimplified picture, one that threads a middle path between absolutism and perspectivalism, a path that considers both frame-dependent or covariant truths and frame-independent or invariant truths and examines the relations between them. Indeed, the notions of covariance and invariance play important roles in the development of the fields of mathematics, physics, philosophy, and psychology in the decades after the turn of the 20th century. The migration of the concepts of invariance and covariance illustrates not only the interconnectedness of the working communities of intellectuals, but also displays ways in which the personal, social, and political overlaps between groups of disciplinary thinkers are essential conduits for the conceptual cross-fertilization that aids in the health of our modern fields of study. [excerpt

Quantum Wall Crossing in N=2 Gauge Theories

We study refined and motivic wall-crossing formulas in N=2 supersymmetric gauge theories with SU(2) gauge group and N_f < 4 matter hypermultiplets in the fundamental representation. Such gauge theories provide an excellent testing ground for the conjecture that "refined = motivic."Comment: 24 pages, 4 figure

Symbolic Tensor Calculus -- Functional and Dynamic Approach

In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached