Bergman's Diamond Lemma for ring theory gives an algorithm to produce a (non-canonical) basis for a ring presented by generators and relations. After demonstrating this algorithm in concrete, geometrically-minded examples, I'll turn to preprojective algebras and their multiplicative counterparts. Using the Diamond Lemma, I'll reprove a few classical results for preprojective algebras. Then I'll propose a conjectural basis for multiplicative preprojective algebras. Finally I'll explain why the set is a basis in the case of...

We argue that, within a broad class of extensions of the Standard Model, there is a tight corellation between the dynamics of the electroweak phase transition and the cubic self-coupling of the Higgs boson: Models which exhibit a strong first-order electroweak phase transition predict a large deviation of the Higgs self-coupling from the Standard Model prediction, as long as no accidental cancellations occur. Order-one deviations are typical. This shift would be observable at the Large...

Using the general structure of the vacuum polarization tensor at non-zero temperature T and finite magnetic field B, the ring contribution to QED effective potential is determined beyond the static (zero momentum) limit. In the limit of weak magnetic field and at high temperature, the improved ring potential consists of a term proportional to T4®5=2, in ad-dition to the well-known T4®3=2 term. In the limit of strong magnetic field, where QED dynamics is dominated by...

Many modified gravity schemes predict a non-zero difference (``gravitational slip\'\') between the Newtonian and longitudinal perturbed metric potentials. Such a slip would affect the growth of large scale structure without altering the expansion history of the universe. We quantify the slip with a new parameter varpi, show the effect of non-zero varpi on the growth of cosmic overdensities, and constrain its value using CMB and weak lensing data.

We study the necessary and sufficient topological conditions for general Calabi-Yaus to get a non-supersymmetric AdS exponentially large volume minimum of the scalar potential in flux compactifications of IIB string theory. It turns out that string loop corrections play a crucial role to realise exponentially large volume minima for fibration Calabi-Yaus and to stabilise 4-cycles which support chiral matter. The robustness of these results is due to the \'extended no-scale structure\': for arbitrary Calabi-Yaus, the...

Moduli stabilization, SUSY breaking and flavor structure are discussed in 5D gauged supergravity models with two vector-multiplet moduli fields. One modulus field makes the fermion mass hierarchy while the other is relevant to the SUSY breaking mediation. We analyse the potential for the moduli from the viewpoint of the 4D effective theory to obtain the stabilized values of the moduli and their F-terms.

Proton structure measurements at high $Q^{2}$ performed by the H1 and ZEUS collaborations at the HERA collider, are reviewed. Neutral and charged current deep inelastic scattering cross sections and structure functions are presented. The review also discusses improvements to the parton density measurements using jet cross section data and recent high $Q^{2}$ inclusive cross section measurements.

Large scale structure contains vastly more Fourier modes than the CMB, and is therefore a promising arena for studying the early universe.  One obstacle to using these modes is the non-linearity of structure formation. The amount of weakly coupled information available is therefore very sensitive to scale at which non-linear effects become important and simulations become necessary.  Using effective field theory techniques, I will present evidence that the perturbative description of dark matter is much...

Impacts of asteroid and comets constitute major geologic processes shaping the surfaces and evolution of planetary bodies. Impacts produce deep transient cavities, with excavation to deep crustal levels, fragmentation, and removal of large rock volumes. Formation of complex craters involves high pressures and temperatures resulting in intense deformation, fracturing and melting. Here, we analyze the crater-forming impacts and their effects on the Earth´s climate, environment and life-support systems, in relation to the Cretaceous/Paleogene (K/Pg) boundary....

Time in quantum mechanics has duly received a lot of attention over the years. Perfect clocks which can turn on/off a particular interaction at a precise time that have been proposed only exist in infinite dimensions and have unphysical Hamiltonians (their spectrum is unbounded from below). It was this observation which led many to conclude that an operator for time cannot exist in quantum mechanics. Here, we prove rigorous results about the accuracy of finite dimensional clocks...

In the last years, the NA48/2 experiment at the CERN SPS has recorded an unprecedented sample of charged kaon decays. From this, we report very precise measurements of fundamental parameters of Chiral Perturbation Theory (ChPT) and the study of low energy pi-pi scattering. Several rare and very rare decays have been studied. From more than 10^6 K+- -> pi+ pi0 gamma decays, a first measurement of the interference between Bremsstrahlung and Direct Emission amplitudes and...

In this expository talk, I describe how "chaotic behavior" not only was discovered in the study of the Newtonian N-body problem, but also is responsible for several strange appearing motions. Then, a mathematical outline of the general evolution of the universe, under Newton's laws, is provided. No prior background in dynamics or the mathematics of the N-body problem is needed to follow this lecture

Quantum Information Theory

Qunatum Information Theory

We present the first year SDSS-II Supernova Survey results and their implications for cosmology and future supernova surveys. We then discuss challenges that face next-generation surveys, such as LSST, which will deliver of order a million supernovae without spectroscopic confirmation. As a way to address these challenges, we introduce BEAMS, a statistical method to do photometric supernova cosmology, and present a preliminary application to SDSS data. Finally we highlight the importance of future surveys such...

Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of the probability calculus and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that an agent’s degrees of belief be coherent. I argue that de Finetti held that the coherence conditions of degrees of...

We explore simple but novel solutions of general relativity which, classically, approximate cosmologies cycling through an infinite set of ``bounces." These solutions require curvature K=+1, and are supported by a negative cosmological term and matter with -1 < w < -1/3. They can be studied within the regime of validity of general relativity. We argue that quantum mechanically, particle production leads eventually to a departure from the regime of validity of semiclassical general relativity, likely...

After a brief overview of the three broad classes of superconducting quantum bits (qubits)--flux, charge and phase--I describe experiments on single and coupled flux qubits. The quantum state of a flux qubit is measured with a Superconducting QUantum Interference Device (SQUID). Single flux qubits exhibit the properties of a spin-1/2 system, including superposition of quantum states, Rabi oscillations and spin echoes. Two qubits, coupled by their mutual inductance and by screening currents in the readout...