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Unwell: The Public Health Implications of Unregulated Drinking Water

By Nate Seltenrich Environmental Health Perspectives Roughly one in seven U.S. residents relies on a private well for drinking water.1 Unlike the rest of the population served by the nation’s many public water systems,2 these 44.5 million Americans are not … Continue reading






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Vert.x ramblings: Asynchronous network, your time has come

With the debut of Vert.x, the asynchronous framework is reaching an inflection point, suggests Andrew Cholakian. With Vert.x, the software is packaged together in such a way as to be extremely practical, he states. For some JVM zealots, Vert.x may meet needs recently and apparently addressed by node.js. Vert.x is an asynchronous application server – Read the rest...






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‘Warning Bells Going Off’ as NOAA Forecasts Entire Great Barrier Reef at Risk of Coral Bleaching and Death

By Jessica Corbett Common Dreams “This is a wake-up call,” says one Australian marine biologist. “Given sea temperatures usually increase as we get towards March, this is probably conservative.” Delivering yet another “wake-up call” after recent studies have shown that … Continue reading





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‘Warning Bells Going Off’ as NOAA Forecasts Entire Great Barrier Reef at Risk of Coral Bleaching and Death

By Jessica Corbett Common Dreams “This is a wake-up call,” says one Australian marine biologist. “Given sea temperatures usually increase as we get towards March, this is probably conservative.” Delivering yet another “wake-up call” after recent studies have shown that … Continue reading




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The future of UX research is automated, and that's a problem

If you compare the UX research methods we use today with the methods we used 16 years ago, something interesting emerges. We see that UX research is becoming increasingly remote and increasingly unmoderated. In other words, we're moving to a world where UX research is becoming automated. We can learn a lot from automated research. But it comes at the price of understanding our users.




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Modern Website Deliverables

You’re hiring a web designer or providing web design services, what’s included in a normal project? In other words, what are the deliverables, and the use of a membership website builder could be essential for this. Let’s start by defining what a deliverable is. Wikipedia defines a deliverable as: …a tangible or intangible good or […]

The post Modern Website Deliverables appeared first on Psychology of Web Design | 3.7 Blog.




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Reestablishing a Social Life on Campus with Other Veterans and Civilians Post-TBI

Transitioning from military to civilian life can take time and can be tricky. Adam talks about how student veteran groups on college campuses can help vets reintegrate socially in their own way and  time.




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BrainLine Military Blogger Adam Anicich Says Thank You and Goodbye for Now

Adam thanks you — his blog viewers and supporters — and encourages you to continue the discussion and awareness raising about TBI and PTSD; the battle does not stop here.




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3 Ways to Optimise Blog Content so it Ranks Well on Google

When it comes to your blog’s position within search engine results, there’s far more than just sheer luck at play. Search Engine Optimisation is a skill that any content creator – professional or amateur – should develop in order to make their content as discoverable as possible. It involves making certain tweaks to your blog […]

Original post: 3 Ways to Optimise Blog Content so it Ranks Well on Google

The post 3 Ways to Optimise Blog Content so it Ranks Well on Google appeared first on Daily Blog Tips.




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Website Inspiration: BlurHash

Clear representation of how the product works in the header of the Landing Page for BlurHash. A BlurHash is a compact representation of a placeholder for an image. When integrated they really improves app designs by replacing boring grey boxes with smoother loading images. Full Review




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Mysterious Sharks Dance Away Bethel's COVID-19 Blues

A couple of mysterious sharks have caught the fancy of the town. Maybe it's the cabin fever finally setting in, or perhaps this is what happens when you go too long without washing your mask, but Bethelites are going wild for two people in inflatable shark suits who pop up randomly around town.




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Top Colorado Republican Pressures Official to Report False Election Results

U.S. Rep. Ken Buck, who is also the chairman of the Colorado Republican Party, was captured ordering a local party official to report false election results in a primary race for a state Senate seat in a leaked audio recording released earlier this week.




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Everything is Figureoutable with Marie Forleo

You know her, the award-winning host, author and speaker, Marie Forleo returns to the podcast to talk about her new book , Everything Is Figureoutable. In the New York Times Best-Selling book, Marie gives readers tactics to look at setbacks positively and overcome obstacles creatively, so you can start reaching your dreams.  In this episode, we sit down to talk about how her life experiences influenced the book. She shares stories of fear, failure and always having fun have impacted her life. And we discuss a quote of hers (that I repeat all the time) that can help you get into the creative zone. Enjoy! FOLLOW MARIE: instagram | twitter | website Listen to the Podcast Subscribe   Watch the Episode  This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, Grammy Award winners, New York Times best selling authors and the best entrepreneurs of our times.

The post Everything is Figureoutable with Marie Forleo appeared first on Chase Jarvis Photography.




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Imagine What’s Possible – On Stage /w Humans of New York Creator Brandon Stanton

My book Creative Calling is out! Thanks for all your love, support, and help getting it out into the world. We kicked off celebrations in Seattle with over 700 people in attendance to talk about Creativity with my good buddy, Humans of New York creator, Brandon Stanton. I recorded the session for you. Hope you enjoy! FOLLOW HUMANS OF NEW YORK: instagram | twitter | website Listen to the Podcast Subscribe   This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, Grammy Award winners, New York Times best selling authors and the best entrepreneurs of our times.

The post Imagine What’s Possible – On Stage /w Humans of New York Creator Brandon Stanton appeared first on Chase Jarvis Photography.




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Resilience and Going Untouchable with Neil Pasricha

Neil Pasricha is a bestselling author and podcaster whose work focuses on topics core to all of our lives: gratitude, happiness, failure, resilience, and trust. He’s the author of six books including The Book of Awesome, The Happiness Equation, Awesome Is Everywhere, and his latest book: You Are Awesome.  In this episode: We are too thin skinned. No matter how great our achievements, we’re crushed by the simplest things. Neil shares some practical advice to navigate through pain and build resiliency Always do something you’re learning… Or as I like to say, how to give yourself permission to suck There’s a reason why they call something a “practice”. We get into how to let go and allow yourself to be human. and much more Enjoy! FOLLOW NEIL: twitter | website Listen to the Podcast Subscribe   This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, Grammy Award winners, New York Times best selling authors and the best entrepreneurs […]

The post Resilience and Going Untouchable with Neil Pasricha appeared first on Chase Jarvis Photography.




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Rethink Impossible with Colin O’Brady

Colin O’Brady is a world record holding explorer and one of the world’s top endurance athletes. Fresh out of college, Colin had a vast world of possibility in front of him when a tragic accident left him hospitalized. Unsure if he’d ever walk again, his injuries covered nearly 25% of his body, primarily damaging his legs and feet. Despite the odds, his mother encouraged him to dream big and he dared to set a seemingly impossible goal that set him on a path to rethink what’s possible. Fast forward to today, and Colin’s list of achievements is staggering. In this episode, we get into many of his harrowing adventures, including his solo, unsupported, unassisted crossing of Antartica. Even if you’re not a professional athlete or have any ambition to break world records, his story will resonate. We all need courage, a strong mindset, and pure grit to overcome obstacles, pursue big dreams, and do the seemingly impossible. A few highlights from our conversation: 1000 NOs paves the way to YES. How failure is only helping us forge and prepare us for the thing we are reaching for. The longest journey is 6 inches between your ears. Colin shares how he discovered mindset […]

The post Rethink Impossible with Colin O’Brady appeared first on Chase Jarvis Photography.




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Getting Comfortable with Being Uncomfortable

Being uncomfortable isn’t usually fun. In fact, we’re probably more likely to try to avoid uncomfortable situations than actually run toward them. Yet, it is a valuable skill. Not only in dealing with adversity but giving us confidence and trust in ourselves to recover quickly from failure, manage our fears, and explore the unknown. In today’s episode, we dive a big deeper into this topic and I share a few ways we can all practice getting comfortable with being uncomfortable. Enjoy! FOLLOW CHASE: instagram | twitter | website Listen to the Podcast Subscribe   This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, Grammy Award winners, New York Times best selling authors and the best entrepreneurs of our times.

The post Getting Comfortable with Being Uncomfortable appeared first on Chase Jarvis Photography.




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Five Aspects of a Successful Blog Post

It’s 2018, and traditional marketing concept has shifted. We often hear that content marketing is taking the top and is the future of marketing. While content marketing doesn’t only mean blogging, blog posts on a product, service or about your business, should be a big part of your content marketing strategy. There are vast amounts …

Five Aspects of a Successful Blog Post Read More »




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The Canon EOS R5 release gets closer as it passes Bluetooth certification

We’re a big step closer to a Canon EOS R5 release announcement now, as Nokishita Tweets that it has passed its Bluetooth certification. The belief is that the EOS R5 was originally scheduled to ship in July, and Canon Rumors reports that they’ve been told that’ll still happen. With lockdowns still in effect in much […]

The post The Canon EOS R5 release gets closer as it passes Bluetooth certification appeared first on DIY Photography.




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Double Chance Picks *** Sunday *** 17 September 2017

We have a new preview on https://www.007soccerpicks.com/sunday-matches/double-chance-picks-sunday-17-september-2017/

Double Chance Picks *** Sunday *** 17 September 2017

DOUBLE CHANCE PICKS To return: ??? USD Odds: 2.80 Stake: 100 USD   Starting in   Teams   Our Prediction Odds Las Palmas - Ath Bilbao Soccer: Spain - LaLiga X2 1.45 Chievo - Atalanta Soccer: Italy - Serie…




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Double Chance Picks *** Monday *** 18 September 2017

We have a new preview on https://www.007soccerpicks.com/monday-matches/double-chance-picks-monday-18-september-2017/

Double Chance Picks *** Monday *** 18 September 2017

DOUBLE CHANCE PICKS To return: ??? USD Odds: 2.03 Stake: 100 USD   Starting in   Teams   Our Prediction Odds Espanyol - Celta Vigo Soccer: Spain - LaLiga 1X 1.29 AFC Eskilstuna - Sundsvall Soccer: Sweden -…




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Double Chance Picks *** Tuesday *** 19 September 2017

We have a new preview on https://www.007soccerpicks.com/tuesday-matches/double-chance-picks-tuesday-19-september-2017/

Double Chance Picks *** Tuesday *** 19 September 2017

DOUBLE CHANCE PICKS To return: ??? USD Odds: 1.95 Stake: 100 USD   Starting in   Teams   Our Prediction Odds Bournemouth - Brighton Soccer: England - Carabao Cup 1X 1.20 Wolfsburg - SV Werder Bremen Soccer: Germany…




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Cameron-Liebler sets in Hamming graphs. (arXiv:2005.02227v2 [math.CO] UPDATED)

In this paper, we discuss Cameron-Liebler sets in Hamming graphs, obtain several equivalent definitions and present all classification results.




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Some Quot schemes in tilted hearts and moduli spaces of stable pairs. (arXiv:2005.02202v2 [math.AG] UPDATED)

For a smooth projective variety $X$, we study analogs of Quot functors in hearts of non-standard $t$-structures of $D^b(mathrm{Coh}(X))$. The technical framework is that of families of $t$-structures, as studied in arXiv:1902.08184. We provide several examples and suggest possible directions of further investigation, as we reinterpret moduli spaces of stable pairs, in the sense of Thaddeus (arXiv:alg-geom/9210007) and Huybrechts-Lehn (arXiv:alg-geom/9211001), as instances of Quot schemes.




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Nonlinear singular problems with indefinite potential term. (arXiv:2005.01789v3 [math.AP] UPDATED)

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator plus an indefinite potential. In the reaction we have the competing effects of a singular term and of concave and convex nonlinearities. In this paper the concave term is parametric. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter $lambda$ varies. This work continues our research published in arXiv:2004.12583, where $xi equiv 0 $ and in the reaction the parametric term is the singular one.




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Solving an inverse problem for the Sturm-Liouville operator with a singular potential by Yurko's method. (arXiv:2004.14721v2 [math.SP] UPDATED)

An inverse spectral problem for the Sturm-Liouville operator with a singular potential from the class $W_2^{-1}$ is solved by the method of spectral mappings. We prove the uniqueness theorem, develop a constructive algorithm for solution, and obtain necessary and sufficient conditions of solvability for the inverse problem in the self-adjoint and the non-self-adjoint cases




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On the exterior Dirichlet problem for a class of fully nonlinear elliptic equations. (arXiv:2004.12660v3 [math.AP] UPDATED)

In this paper, we mainly establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for a class of fully nonlinear second-order elliptic equations related to the eigenvalues of the Hessian, with prescribed generalized symmetric asymptotic behavior at infinity. Moreover, we give some new results for the Hessian equations, Hessian quotient equations and the special Lagrangian equations, which have been studied previously.




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Set-Theoretical Problems in Asymptology. (arXiv:2004.01979v3 [math.GN] UPDATED)

In this paper we collect some open set-theoretic problems that appear in the large-scale topology (called also Asymptology). In particular we ask problems about critical cardinalities of some special (large, indiscrete, inseparated) coarse structures on $omega$, about the interplay between properties of a coarse space and its Higson corona, about some special ultrafilters ($T$-points and cellular $T$-points) related to finitary coarse structures on $omega$, about partitions of coarse spaces into thin pieces, and also about coarse groups having some extremal properties.




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On boundedness, gradient estimate, blow-up and convergence in a two-species and two-stimuli chemotaxis system with/without loop. (arXiv:1909.04587v4 [math.AP] UPDATED)

In this work, we study dynamic properties of classical solutions to a homogenous Neumann initial-boundary value problem (IBVP) for a two-species and two-stimuli chemotaxis model with/without chemical signalling loop in a 2D bounded and smooth domain. We successfully detect the product of two species masses as a feature to determine boundedness, gradient estimates, blow-up and $W^{j,infty}(1leq jleq 3)$-exponential convergence of classical solutions for the corresponding IBVP. More specifically, we first show generally a smallness on the product of both species masses, thus allowing one species mass to be suitably large, is sufficient to guarantee global boundedness, higher order gradient estimates and $W^{j,infty}$-convergence with rates of convergence to constant equilibria; and then, in a special case, we detect a straight line of masses on which blow-up occurs for large product of masses. Our findings provide new understandings about the underlying model, and thus, improve and extend greatly the existing knowledge relevant to this model.




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Decentralized and Parallelized Primal and Dual Accelerated Methods for Stochastic Convex Programming Problems. (arXiv:1904.09015v10 [math.OC] UPDATED)

We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles the proposed methods are optimal in terms of the number of communication steps. However, for all classes of the objective, the optimality in terms of the number of oracle calls per node in the class of methods with optimal number of communication steps takes place only up to a logarithmic factor and the notion of smoothness. By using mini-batching technique we show that all proposed methods with stochastic oracle can be additionally parallelized at each node.




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Categorification via blocks of modular representations for sl(n). (arXiv:1612.06941v3 [math.RT] UPDATED)

Bernstein, Frenkel, and Khovanov have constructed a categorification of tensor products of the standard representation of $mathfrak{sl}_2$, where they use singular blocks of category $mathcal{O}$ for $mathfrak{sl}_n$ and translation functors. Here we construct a positive characteristic analogue using blocks of representations of $mathfrak{sl}_n$ over a field $ extbf{k}$ of characteristic $p$ with zero Frobenius character, and singular Harish-Chandra character. We show that the aforementioned categorification admits a Koszul graded lift, which is equivalent to a geometric categorification constructed by Cautis, Kamnitzer, and Licata using coherent sheaves on cotangent bundles to Grassmanians. In particular, the latter admits an abelian refinement. With respect to this abelian refinement, the stratified Mukai flop induces a perverse equivalence on the derived categories for complementary Grassmanians. This is part of a larger project to give a combinatorial approach to Lusztig's conjectures for representations of Lie algebras in positive characteristic.




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Word problems for finite nilpotent groups. (arXiv:2005.03634v1 [math.GR])

Let $w$ be a word in $k$ variables. For a finite nilpotent group $G$, a conjecture of Amit states that $N_w(1) ge |G|^{k-1}$, where $N_w(1)$ is the number of $k$-tuples $(g_1,...,g_k)in G^{(k)}$ such that $w(g_1,...,g_k)=1$. Currently, this conjecture is known to be true for groups of nilpotency class 2. Here we consider a generalized version of Amit's conjecture, and prove that $N_w(g) ge |G|^{k-2}$, where $g$ is a $w$-value in $G$, for finite groups $G$ of odd order and nilpotency class 2. If $w$ is a word in two variables, we further show that $N_w(g) ge |G|$, where $g$ is a $w$-value in $G$ for finite groups $G$ of nilpotency class 2. In addition, for $p$ a prime, we show that finite $p$-groups $G$, with two distinct irreducible complex character degrees, satisfy the generalized Amit conjecture for words $w_k =[x_1,y_1]...[x_k,y_k]$ with $k$ a natural number; that is, for $g$ a $w_k$-value in $G$ we have $N_{w_k}(g) ge |G|^{2k-1}$.

Finally, we discuss the related group properties of being rational and chiral, and show that every finite group of nilpotency class 2 is rational.




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On products of groups and indices not divisible by a given prime. (arXiv:2005.03608v1 [math.GR])

Let the group $G = AB$ be the product of subgroups $A$ and $B$, and let $p$ be a prime. We prove that $p$ does not divide the conjugacy class size (index) of each $p$-regular element of prime power order $xin Acup B$ if and only if $G$ is $p$-decomposable, i.e. $G=O_p(G) imes O_{p'}(G)$.




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Steiner symmetry in the minimization of the principal positive eigenvalue of an eigenvalue problem with indefinite weight. (arXiv:2005.03581v1 [math.AP])

In cite{CC} the authors, investigating a model of population dynamics, find the following result. Let $Omegasubset mathbb{R}^N$, $Ngeq 1$, be a bounded smooth domain. The weighted eigenvalue problem $-Delta u =lambda m u $ in $Omega$ under homogeneous Dirichlet boundary conditions, where $lambda in mathbb{R}$ and $min L^infty(Omega)$, is considered. The authors prove the existence of minimizers $check m$ of the principal positive eigenvalue $lambda_1(m)$ when $m$ varies in a class $mathcal{M}$ of functions where average, maximum, and minimum values are given. A similar result is obtained in cite{CCP} when $m$ is in the class $mathcal{G}(m_0)$ of rearrangements of a fixed $m_0in L^infty(Omega)$. In our work we establish that, if $Omega$ is Steiner symmetric, then every minimizer in cite{CC,CCP} inherits the same kind of symmetry.




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Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces. (arXiv:2005.03494v1 [math.CA])

We consider the most general class of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of an arbitrary order whose solutions and right-hand sides belong to appropriate Sobolev spaces. For parameter-dependent problems from this class, we prove a constructive criterion for their solutions to be continuous in the Sobolev space with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of these solutions to the solution of the nonperturbed problem.




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On the connection problem for the second Painlev'e equation with large initial data. (arXiv:2005.03440v1 [math.CA])

We consider two special cases of the connection problem for the second Painlev'e equation (PII) using the method of uniform asymptotics proposed by Bassom et al.. We give a classification of the real solutions of PII on the negative (positive) real axis with respect to their initial data. By product, a rigorous proof of a property associate with the nonlinear eigenvalue problem of PII on the real axis, recently revealed by Bender and Komijani, is given by deriving the asymptotic behavior of the Stokes multipliers.




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Removable singularities for Lipschitz caloric functions in time varying domains. (arXiv:2005.03397v1 [math.CA])

In this paper we study removable singularities for regular $(1,1/2)$-Lipschitz solutions of the heat equation in time varying domains. We introduce an associated Lipschitz caloric capacity and we study its metric and geometric properties and the connection with the $L^2$ boundedness of the singular integral whose kernel is given by the gradient of the fundamental solution of the heat equation.




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Maximum of Exponential Random Variables, Hurwitz's Zeta Function, and the Partition Function. (arXiv:2005.03392v1 [math.PR])

A natural problem in the context of the coupon collector's problem is the behavior of the maximum of independent geometrically distributed random variables (with distinct parameters). This question has been addressed by Brennan et al. (British J. of Math. & CS. 8 (2015), 330-336). Here we provide explicit asymptotic expressions for the moments of that maximum, as well as of the maximum of exponential random variables with corresponding parameters. We also deal with the probability of each of the variables being the maximal one.

The calculations lead to expressions involving Hurwitz's zeta function at certain special points. We find here explicitly the values of the function at these points. Also, the distribution function of the maximum we deal with is closely related to the generating function of the partition function. Thus, our results (and proofs) rely on classical results pertaining to the partition function.




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A reducibility problem for even Unitary groups: The depth zero case. (arXiv:2005.03386v1 [math.RT])

We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ a quadratic extension of p-adic fields the associated unitary group $G=mathrm{U}(n,n)$ contains a parabolic subgroup $P$ with Levi component $L$ isomorphic to $mathrm{GL}_n(E)$. Let $pi$ be an irreducible supercuspidal representation of $L$ of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation $iota_P^G pi$ is reducible.




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A theory of stacks with twisted fields and resolution of moduli of genus two stable maps. (arXiv:2005.03384v1 [math.AG])

We construct a smooth moduli stack of tuples consisting of genus two nodal curves, line bundles, and twisted fields. It leads to a desingularization of the moduli of genus two stable maps to projective spaces. The construction of this new moduli is based on systematical application of the theory of stacks with twisted fields (STF), which has its prototype appeared in arXiv:1906.10527 and arXiv:1201.2427 and is fully developed in this article. The results of this article are the second step of a series of works toward the resolutions of the moduli of stable maps of higher genera.




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A Schur-Nevanlinna type algorithm for the truncated matricial Hausdorff moment problem. (arXiv:2005.03365v1 [math.CA])

The main goal of this paper is to achieve a parametrization of the solution set of the truncated matricial Hausdorff moment problem in the non-degenerate and degenerate situation. We treat the even and the odd cases simultaneously. Our approach is based on Schur analysis methods. More precisely, we use two interrelated versions of Schur-type algorithms, namely an algebraic one and a function-theoretic one. The algebraic version, worked out in our former paper arXiv:1908.05115, is an algorithm which is applied to finite or infinite sequences of complex matrices. The construction and discussion of the function-theoretic version is a central theme of this paper. This leads us to a complete description via Stieltjes transform of the solution set of the moment problem under consideration. Furthermore, we discuss special solutions in detail.




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Lorentz estimates for quasi-linear elliptic double obstacle problems involving a Schr"odinger term. (arXiv:2005.03281v1 [math.AP])

Our goal in this article is to study the global Lorentz estimates for gradient of weak solutions to $p$-Laplace double obstacle problems involving the Schr"odinger term: $-Delta_p u + mathbb{V}|u|^{p-2}u$ with bound constraints $psi_1 le u le psi_2$ in non-smooth domains. This problem has its own interest in mathematics, engineering, physics and other branches of science. Our approach makes a novel connection between the study of Calder'on-Zygmund theory for nonlinear Schr"odinger type equations and variational inequalities for double obstacle problems.




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The Congruence Subgroup Problem for finitely generated Nilpotent Groups. (arXiv:2005.03263v1 [math.GR])

The congruence subgroup problem for a finitely generated group $Gamma$ and $Gleq Aut(Gamma)$ asks whether the map $hat{G} o Aut(hat{Gamma})$ is injective, or more generally, what is its kernel $Cleft(G,Gamma ight)$? Here $hat{X}$ denotes the profinite completion of $X$. In the case $G=Aut(Gamma)$ we denote $Cleft(Gamma ight)=Cleft(Aut(Gamma),Gamma ight)$.

Let $Gamma$ be a finitely generated group, $ar{Gamma}=Gamma/[Gamma,Gamma]$, and $Gamma^{*}=ar{Gamma}/tor(ar{Gamma})congmathbb{Z}^{(d)}$. Denote $Aut^{*}(Gamma)= extrm{Im}(Aut(Gamma) o Aut(Gamma^{*}))leq GL_{d}(mathbb{Z})$. In this paper we show that when $Gamma$ is nilpotent, there is a canonical isomorphism $Cleft(Gamma ight)simeq C(Aut^{*}(Gamma),Gamma^{*})$. In other words, $Cleft(Gamma ight)$ is completely determined by the solution to the classical congruence subgroup problem for the arithmetic group $Aut^{*}(Gamma)$.

In particular, in the case where $Gamma=Psi_{n,c}$ is a finitely generated free nilpotent group of class $c$ on $n$ elements, we get that $C(Psi_{n,c})=C(mathbb{Z}^{(n)})={e}$ whenever $ngeq3$, and $C(Psi_{2,c})=C(mathbb{Z}^{(2)})=hat{F}_{omega}$ = the free profinite group on countable number of generators.




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On the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph. (arXiv:2005.03259v1 [math.CO])

In this paper, we give a criterion of the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ is Gorenstein if and only if (1) sizes of maximal cliques are constant (say $n$) and (2) (a) $n=1$, (b) $n=2$ and there is no odd cycle without chord and length at least 7 or (c) $ngeq 3$ and there is no odd cycle without chord and length at least 5.




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The UCT problem for nuclear $C^ast$-algebras. (arXiv:2005.03184v1 [math.OA])

In recent years, a large class of nuclear $C^ast$-algebras have been classified, modulo an assumption on the Universal Coefficient Theorem (UCT). We think this assumption is redundant and propose a strategy for proving it. Indeed, following the original proof of the classification theorem, we propose bridging the gap between reduction theorems and examples. While many such bridges are possible, various approximate ideal structures appear quite promising.