Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order to clarify some amb...Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order to clarify some ambiguity, we sharpen the definition of PL minimal surfaces, and prove a technical lemma on the Plateau problem in the hyperbolic space.展开更多
On September 23, the 2016 Lasker-DeBakey clinical medical research award ceremony was celebrated in New York City. This annual prize has been awarded by the Lasker Foundation for over 71 years, and it is the most pres...On September 23, the 2016 Lasker-DeBakey clinical medical research award ceremony was celebrated in New York City. This annual prize has been awarded by the Lasker Foundation for over 71 years, and it is the most prestigious biomedical award in the United States, popu- larly known as "America's Nobel Prize". Indeed, 87 Lasker laureates have received the Nobel Prize, including 41 within the last 30 years (one example is the Chinese pharmaceutical chemist Youyou Tu, who won the 2011 Lasker-DeBakey award and four years later received the Nobel Prize). This year, the honor went to Ralf F. W. Bartenschlager (Heidelberg University, Germany), Charles M. Rice (Rockefeller University, NY, USA), and Michael J. Sofia (Arbutus Biopharma, PA, USA) for the development of cell culture system to study the replication of Hepatitis C virus (HCV) and for the use of this system to develop drugs capable of eliminating Hepatitis C.展开更多
Let K be a genus g alternating knot with Alexander polynomial Δ_(K)(T)=Σ_(i=-g)^(g)a_(i)T^(i).We show that if |a_(g)|=|a_(g-1)|,then K is the torus knot T_(2g+1,±2).This is a special case of the Fox Trapezoidal...Let K be a genus g alternating knot with Alexander polynomial Δ_(K)(T)=Σ_(i=-g)^(g)a_(i)T^(i).We show that if |a_(g)|=|a_(g-1)|,then K is the torus knot T_(2g+1,±2).This is a special case of the Fox Trapezoidal Conjecture.The proof uses Ozsvath and Szabo's work on alternating knots.展开更多
Using an argument of Baldwin-Hu-Sivek,we prove that if K is a hyperbolic fibered knot with fiber F in a closed,oriented 3-manifold Y,andHFK(Y,K,[F],g(F)−1)has rank 1,then the monodromy of K is freely isotopic to a pse...Using an argument of Baldwin-Hu-Sivek,we prove that if K is a hyperbolic fibered knot with fiber F in a closed,oriented 3-manifold Y,andHFK(Y,K,[F],g(F)−1)has rank 1,then the monodromy of K is freely isotopic to a pseudo-Anosov map with no fixed points.In particular,this shows that the monodromy of a hyperbolic L-space knot is freely isotopic to a map with no fixed points.展开更多
基金the Centennial fellowship of the Graduate School at Princeton University
文摘Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order to clarify some ambiguity, we sharpen the definition of PL minimal surfaces, and prove a technical lemma on the Plateau problem in the hyperbolic space.
文摘On September 23, the 2016 Lasker-DeBakey clinical medical research award ceremony was celebrated in New York City. This annual prize has been awarded by the Lasker Foundation for over 71 years, and it is the most prestigious biomedical award in the United States, popu- larly known as "America's Nobel Prize". Indeed, 87 Lasker laureates have received the Nobel Prize, including 41 within the last 30 years (one example is the Chinese pharmaceutical chemist Youyou Tu, who won the 2011 Lasker-DeBakey award and four years later received the Nobel Prize). This year, the honor went to Ralf F. W. Bartenschlager (Heidelberg University, Germany), Charles M. Rice (Rockefeller University, NY, USA), and Michael J. Sofia (Arbutus Biopharma, PA, USA) for the development of cell culture system to study the replication of Hepatitis C virus (HCV) and for the use of this system to develop drugs capable of eliminating Hepatitis C.
文摘Let K be a genus g alternating knot with Alexander polynomial Δ_(K)(T)=Σ_(i=-g)^(g)a_(i)T^(i).We show that if |a_(g)|=|a_(g-1)|,then K is the torus knot T_(2g+1,±2).This is a special case of the Fox Trapezoidal Conjecture.The proof uses Ozsvath and Szabo's work on alternating knots.
基金The author was partially supported by NSF Grant Number DMS-1811900.
文摘Using an argument of Baldwin-Hu-Sivek,we prove that if K is a hyperbolic fibered knot with fiber F in a closed,oriented 3-manifold Y,andHFK(Y,K,[F],g(F)−1)has rank 1,then the monodromy of K is freely isotopic to a pseudo-Anosov map with no fixed points.In particular,this shows that the monodromy of a hyperbolic L-space knot is freely isotopic to a map with no fixed points.