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With María Medina de la Torre and Enrico Valdinoci, Dipierro is a coauthor of the monograph Fractional Elliptic Problems with Critical Growth in the Whole of (arXiv : 1506.01748; Edizioni Della Normale, 2017). [6]
Serena Dipierro is an Italian mathematician whose research involves partial differential equations, the regularity of their solution, their phase transitions, nonlocal operators, and free boundary problems, with applications including population dynamics, quantum mechanics, crystallography, and mathematical finance. [1] [2] She is a professor in the School of Physics, Mathematics and Computing at the University of Western Australia, where she heads the department of mathematics and statistics. [3]
After earning a laurea at the University of Bari in 2006, and a master's degree with Lorenzo D’Ambrosio at the same university in 2008, [4] Dipierro finished a Ph.D. in mathematics at the International School for Advanced Studies in Trieste in 2012. Her dissertation, Concentration phenomena for singularly perturbed elliptic problems and related topics, was supervised by Andrea Malchiodi. [5]
She was a postdoctoral researcher at the University of Chile and University of Edinburgh, and a Humboldt Fellow, and a faculty member at the University of Melbourne and University of Milan before taking her present position at the University of Western Australia in 2018. [3]
With María Medina de la Torre and Enrico Valdinoci, Dipierro is a coauthor of the monograph Fractional Elliptic Problems with Critical Growth in the Whole of (arXiv : 1506.01748; Edizioni Della Normale, 2017). [6]
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography to provide equivalent security.
In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or "rough" sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.
In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths.
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function where U is an open subset of that satisfies Laplace's equation, that is,
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point. Closure under addition and subtraction means that a lattice must be a subgroup of the additive group of the points in the space, and the requirements of minimum and maximum distance can be summarized by saying that a lattice is a Delone set. More abstractly, a lattice can be described as a free abelian group of dimension which spans the vector space . For any basis of , the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice, and every lattice can be formed from a basis in this way. A lattice may be viewed as a regular tiling of a space by a primitive cell.
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, i.e. a Banach space. Intuitively, a Sobolev space is a space of functions possessing sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function.
In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication is replaced with ordinary addition:
Mathai Varghese is a mathematician at the University of Adelaide. His first most influential contribution is the Mathai–Quillen formalism, which he formulated together with Daniel Quillen, and which has since found applications in index theory and topological quantum field theory. He was appointed a full professor in 2006. He was appointed Director of the Institute for Geometry and its Applications in 2009. In 2011, he was elected a Fellow of the Australian Academy of Science. In 2013, he was appointed the Elder Professor of Mathematics at the University of Adelaide, and was elected a Fellow of the Royal Society of South Australia. In 2017, he was awarded an ARC Australian Laureate Fellowship. In 2021, he was awarded the prestigious Hannan Medal and Lecture from the Australian Academy of Science, recognizing an outstanding career in Mathematics. In 2021, he was also awarded the prestigious George Szekeres Medal which is the Australian Mathematical Society’s most prestigious medal, recognising research achievement and an outstanding record of promoting and supporting the discipline.
In convex analysis and the calculus of variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima, but need not actually be convex. Informally, a differentiable function is pseudoconvex if it is increasing in any direction where it has a positive directional derivative. The property must hold in all of the function domain, and not only for nearby points.
Maryam Mirzakhani was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. On 13 August 2014, Mirzakhani was honored with the Fields Medal, the most prestigious award in mathematics, becoming the first woman to win the prize, as well as the first Iranian. The award committee cited her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces".
Noriko Yui is a professor of mathematics at Queen's University in Kingston, Ontario.
In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions. A linear program can be regarded as a special case of a linear-fractional program in which the denominator is the constant function 1.
In applied mathematics, Arnold diffusion is the phenomenon of instability of integrable Hamiltonian systems. The phenomenon is named after Vladimir Arnold who was the first to publish a result in the field in 1964. More precisely, Arnold diffusion refers to results asserting the existence of solutions to nearly integrable Hamiltonian systems that exhibit a significant change in the action variables.
In mathematical analysis, the Pólya–Szegő inequality states that the Sobolev energy of a function in a Sobolev space does not increase under symmetric decreasing rearrangement. The inequality is named after the mathematicians George Pólya and Gábor Szegő.
In mathematics, the Hopf lemma, named after Eberhard Hopf, states that if a continuous real-valued function in a domain in Euclidean space with sufficiently smooth boundary is harmonic in the interior and the value of the function at a point on the boundary is greater than the values at nearby points inside the domain, then the derivative of the function in the direction of the outward pointing normal is strictly positive. The lemma is an important tool in the proof of the maximum principle and in the theory of partial differential equations. The Hopf lemma has been generalized to describe the behavior of the solution to an elliptic problem as it approaches a point on the boundary where its maximum is attained.
In mathematics, and in particular in mathematical analysis, the Gagliardo–Nirenberg interpolation inequality is a result in the theory of Sobolev spaces that relates the -norms of different weak derivatives of a function through an interpolation inequality. The theorem is of particular importance in the framework of elliptic partial differential equations and was originally formulated by Emilio Gagliardo and Louis Nirenberg in 1958. The Gagliardo-Nirenberg inequality has found numerous applications in the investigation of nonlinear partial differential equations, and has been generalized to fractional Sobolev spaces by Haim Brezis and Petru Mironescu in the late 2010s.
Gigliola Staffilani is an Italian-American mathematician who works as the Abby Rockefeller Mauze Professor of Mathematics at the Massachusetts Institute of Technology. Her research concerns harmonic analysis and partial differential equations, including the Korteweg–de Vries equation and Schrödinger equation.
Neena Gupta is a professor at the Statistics and Mathematics Unit of the Indian Statistical Institute (ISI), Kolkata. Her primary fields of interest are commutative algebra and affine algebraic geometry.
In mathematics, the fractional Laplacian is an operator, which generalizes the notion of Laplacian spatial derivatives to fractional powers. This operator is often used to generalise certain types of Partial differential equation, two examples are and which both take known PDEs containing the Laplacian and replacing it with the fractional version.
Jennifer Shyamala Sayaka Balakrishnan is an American mathematician known for leading a team that solved the problem of the "cursed curve", a Diophantine equation that was known for being "famously difficult". More generally, Balakrishnan specializes in algorithmic number theory and arithmetic geometry. She is the Clare Boothe Luce Associate Professor at Boston University.
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