KPZ LINE ENSEMBLE IVAN CORWIN AND ALAN HAMMOND Abstract. For each t ≥ 1 we construct an N-indexed ensemble of random continuous curves with three properties: (1) The lowest indexed curve is distributed as the time t Ho

Source URL: www.stats.ox.ac.uk

ON A QUESTION OF ZANNIER NICHOLAS M. KATZ 1. Zannier’s questions We fix an integer N ≥ 1 and an elliptic curve E over Z[1/6N ], given by an equation

Source URL: web.math.princeton.edu

DEFINITE INTEGRATION Rb 5 minute review. Briefly recap why I = a f (x)dx = F (b) − F (a), where dF dx = f . Split the area under a curve into n equal-width bars of width h = (b − a)/n. Show that

Source URL: engmaths.group.shef.ac.uk

RIGHT TURN FARM MACHINERY SIDE ROAD DIVIDED HIGHWAY ENDS NO PASSING ZONE CURVE RIGHT HILL SLIPPERY WHEN WET BIKE CROSSING STOP AHEAD WINDING ROAD SOFT SHOULDER CROSS ROAD S C H O O L C R O S S I N G CAROLINA DEL NORTE

Source URL: www.ncdot.gov

RIGHT TURN FARM MACHINERY SIDE ROAD DIVIDED HIGHWAY ENDS NO PASSING ZONE CURVE RIGHT HILL SLIPPERY WHEN WET BIKE CROSSING STOP AHEAD WINDING ROAD SOFT SHOULDER CROSS ROAD S C H O O L C R O S S I N G CAROLINA DEL NORTE

Source URL: www.ncdot.gov

SMOOTH NUMBERS AND THE QUADRATIC SIEVE Carl Pomerance When faced with a large number n to factor, what do you do first? You might say “Look at the last digit,” with the idea of cheaply pulling out possible factors of

Source URL: www.mat.uniroma2.it

• Mathematics
• Integer factorization algorithms
• Number theory
• Quadratic sieve
• Special number field sieve
• Quadratic residue
• General number field sieve
• Prime number
• Lenstra elliptic curve factorization
• Sieve of Eratosthenes
• Euclidean algorithm
• Prime-counting function

The set of non-n-th powers in a number field is diophantine Joint work with Jan Van Geel (Gent) Jean-Louis Colliot-Th´el`ene (CNRS et Universit´e Paris-Sud, Orsay, visiting BICMR) Capital Normal University

Source URL: www.math.u-psud.fr

• Abstract algebra
• Algebra
• Geometry
• Algebraic geometry
• Algebraic varieties
• Projective geometry
• Smooth scheme
• Projective variety
• Field extension
• Elliptic curve
• Affine variety
• Morphism of algebraic varieties

HYPERSURFACES WITH DEGENERATE DUALS AND THE GEOMETRIC COMPLEXITY THEORY PROGRAM J.M. LANDSBERG, LAURENT MANIVEL AND NICOLAS RESSAYRE Abstract. We determine set-theoretic defining equations for the variety Dualk,d,N ⊂ P

Source URL: www.math.tamu.edu

• Algebra
• Mathematics
• Linear algebra
• Matrix theory
• Determinant
• Morphism of algebraic varieties
• Skew-symmetric matrix
• Matrix
• Algebraic curve
• Semi-invariant of a quiver

A Spring in Imaginary Time Jeff Morton 1. If we have a spring with fixed ends tracing a curve q in n whose energy is E as given, we find that taking the variation of E gives:
Rs

Source URL: math.ucr.edu

• Physics
• Dynamical systems
• Calculus of variations
• Rigid bodies
• Principles
• Rigid body dynamics
• Rotational symmetry
• Principle of least action
• Potential energy
• Generalized coordinates
• Lagrangian mechanics

Component Groups of Quotients of J0 (N ) David Kohel1 and William A. Stein2 1 University of Sydney http://www.maths.usyd.edu.au:8000/u/kohel/

Source URL: iml.univ-mrs.fr

• Mathematics
• Geometry
• Abstract algebra
• Modular forms
• Algebraic curves
• Riemann surfaces
• Analytic number theory
• Elliptic curves
• Hecke operator
• Modular curve
• Modular elliptic curve
• Supersingular elliptic curve